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<h2>SL Paper 2</h2><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(A = ){\text{ }}\pi {r^2} + 2\pi rh"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi rh"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Units <strong>not </strong>required.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000 = \pi {r^2}h"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}h"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> equating to their part (b).</p>
<p>Do not accept unless <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = \pi {r^2}h"> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> is explicitly defined as their part (b).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> into a <strong>correct </strong>part (a).</p>
<p>Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh = \frac{{500\,000}}{r}"> <mi>π</mi> <mi>r</mi> <mi>h</mi> <mo>=</mo> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> and substituting for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh"> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> in expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The conclusion, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>, must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{10^6}"> <mrow> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></span> as equivalent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{1\,000\,000}"> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r"> <mn>2</mn> <mi>π</mi> <mi>r</mi> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{r^2}}}"> <mfrac> <mn>1</mn> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^{ - 2}}"> <mrow> <msup> <mi>r</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {\text{1}}\,{\text{000}}\,{\text{000}}"> <mo>−</mo> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{1\,000\,000}}{{2\pi }}"> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}"> <mi>r</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for isolating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch of derivative function <strong><em>(M1)</em></strong></p>
<p>with its zero indicated <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>54.2</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}"> <mi>π</mi> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )"> <mo>=</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>700</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27\,679.0 \ldots }}{{2000}}"> <mfrac> <mrow> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> </mrow> <mrow> <mn>2000</mn> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by 2000.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 13.8395 \ldots "> <mo>=</mo> <mn>13.8395</mn> <mo>…</mo> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (g).</p>
<p> </p>
<p>14 (cans) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13.8395 \ldots "> <mn>13.8395</mn> <mo>…</mo> </math></span> to the next integer.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability of drawing three blue marbles.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the probability of drawing three white marbles is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{6}"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The bag contains a total of ten marbles of which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span> are white. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Jill plays the game nine times. Find the probability that she wins exactly two prizes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X)"> <mrow> <mtext>E</mtext> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </math></span> formula <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0(p) + 1(0.5) + 2(0.3) + 3(q) = 1.2"> <mn>0</mn> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mo stretchy="false">(</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mn>0.3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>3</mn> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1.2</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = \frac{1}{{30}}"> <mi>q</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>30</mn> </mrow> </mfrac> </math></span>, 0.0333 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of summing probabilities to 1 <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p + 0.5 + 0.3 + q = 1"> <mi>p</mi> <mo>+</mo> <mn>0.5</mn> <mo>+</mo> <mn>0.3</mn> <mo>+</mo> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{1}{6},{\text{ }}0.167"> <mi>p</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.167</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P (3 blue)}} = \frac{1}{{30}},{\text{ }}0.0333"> <mrow> <mtext>P (3 blue)</mtext> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>30</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.0333</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid reasoning <strong><em>R1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P (3 white)}} = {\text{P(0 blue)}}"> <mrow> <mtext>P (3 white)</mtext> </mrow> <mo>=</mo> <mrow> <mtext>P(0 blue)</mtext> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(3 white)}} = \frac{1}{6}"> <mrow> <mtext>P(3 white)</mtext> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span> <strong><em>AG</em></strong> <strong><em>N0</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid method <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(3 white)}} = \frac{w}{{10}} \times \frac{{w - 1}}{9} \times \frac{{w - 2}}{8},{\text{ }}\frac{{_w{C_3}}}{{_{10}{C_3}}}"> <mrow> <mtext>P(3 white)</mtext> </mrow> <mo>=</mo> <mfrac> <mi>w</mi> <mrow> <mn>10</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>9</mn> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>2</mn> </mrow> <mn>8</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <msub> <mi></mi> <mi>w</mi> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> <mrow> <msub> <mi></mi> <mrow> <mn>10</mn> </mrow> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> </mfrac> </math></span></p>
<p>correct equation <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{w}{{10}} \times \frac{{w - 1}}{9} \times \frac{{w - 2}}{8} = \frac{1}{6},{\text{ }}\frac{{_w{C_3}}}{{_{10}{C_3}}} = 0.167"> <mfrac> <mi>w</mi> <mrow> <mn>10</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>9</mn> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>2</mn> </mrow> <mn>8</mn> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <msub> <mi></mi> <mi>w</mi> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> <mrow> <msub> <mi></mi> <mrow> <mn>10</mn> </mrow> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.167</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 6"> <mi>w</mi> <mo>=</mo> <mn>6</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(n,{\text{ }}p),{\text{ }}\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{q^{n - r}},{\text{ }}{(0.167)^2}{(0.833)^7},{\text{ }}\left( {\begin{array}{*{20}{c}} 9 \\ 2 \end{array}} \right)"> <mrow> <mtext>B</mtext> </mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>p</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>n</mi> </mtd> </mtr> <mtr> <mtd> <mi>r</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mi>p</mi> <mi>r</mi> </msup> </mrow> <mrow> <msup> <mi>q</mi> <mrow> <mi>n</mi> <mo>−</mo> <mi>r</mi> </mrow> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>0.167</mn> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>0.833</mn> <msup> <mo stretchy="false">)</mo> <mn>7</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>9</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>0.279081</p>
<p>0.279 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing one prize in first seven attempts <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right),{\text{ }}{\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6}"> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> </math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right){\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6},{\text{ }}0.390714"> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.390714</mn> </math></span></p>
<p>correct approach <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right){\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6} \times \frac{1}{6}"> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> <mo>×</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span></p>
<p>0.065119</p>
<p>0.0651 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the probability distribution of a discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \geqslant 0">
<mi>a</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \geqslant 0">
<mi>b</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 0.3 - a"> <mi>b</mi> <mo>=</mo> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference between the greatest possible expected value and the least possible expected value.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct approach <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">A1</span></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 0.5 + b + a = 1"> <mn>0.2</mn> <mo>+</mo> <mn>0.5</mn> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.7 + a + b = 1"> <mn>0.7</mn> <mo>+</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 0.3 - a"> <mi>b</mi> <mo>=</mo> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </math></span> <em><strong>AG</strong></em><em><strong> N0</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 4 \times 0.5 + a \times b + \left( {a + b - 0.5} \right) \times a"> <mn>0.2</mn> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mn>0.5</mn> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mn>0.5</mn> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>a</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 2 + a \times b - 0.2a"> <mn>0.2</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>−</mo> <mn>0.2</mn> <mi>a</mi> </math></span></p>
<p>valid attempt to express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> in one variable <em><strong>M1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 4 \times 0.5 + a \times \left( {0.3 - a} \right) + \left( { - 0.2} \right) \times a"> <mn>0.2</mn> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mn>0.5</mn> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>0.2</mn> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>a</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.2 + 0.1a - {a^2}"> <mn>2.2</mn> <mo>+</mo> <mn>0.1</mn> <mi>a</mi> <mo>−</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mrow> </math>,</span></p>
<p><em> </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 4 \times 0.5 + \left( {0.3 - b} \right) \times b + \left( { - 0.2} \right) \times \left( {0.3 - b} \right)"> <mn>0.2</mn> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mn>0.5</mn> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>−</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>b</mi> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>0.2</mn> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>−</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.14 + 0.5b - {b^2}"> <mn>2.14</mn> <mo>+</mo> <mn>0.5</mn> <mi>b</mi> <mo>−</mo> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p>correct value of greatest <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.2025"> <mn>2.2025</mn> </math></span> (exact)</p>
<p>valid attempt to find least value <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph with minimum indicated, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( 0 \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </math></span> <strong>and </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( {0.3} \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><em> </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0{\text{, }}2.2} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.2</mn> </mrow> <mo>)</mo> </mrow> </math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0.3{\text{, }}2.14} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.14</mn> </mrow> <mo>)</mo> </mrow> </math></span> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span></p>
<p><em> </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0{\text{, }}2.14} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.14</mn> </mrow> <mo>)</mo> </mrow> </math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0.3{\text{, }}2.2} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.2</mn> </mrow> <mo>)</mo> </mrow> </math></span> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span></p>
<p>correct value of least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.14"> <mn>2.14</mn> </math></span> (exact)</p>
<p>difference <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="= 0.0625"> <mo>=</mo> <mn>0.0625</mn> </math></span> (exact) <em><strong>A1</strong></em><em><strong> N2</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The time it takes Suzi to drive from home to work each morning is normally distributed with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn></math> minutes and a standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> minutes.</p>
<p>On <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math> of days, it takes Suzi longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math> minutes to drive to work.</p>
</div>
<div class="specification">
<p>Suzi will be late to work if it takes her longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes to drive to work. The time it takes to drive to work each day is independent of any other day.</p>
<p>Suzi will work five days next week.</p>
</div>
<div class="specification">
<p>Suzi will work <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn></math> days this month. She will receive a bonus if she is on time at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> of those days.</p>
<p>So far this month, she has worked <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> days and been on time <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> of those days.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On a randomly selected day, find the probability that Suzi’s drive to work will take longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that she will be late to work at least one day next week.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that Suzi will be late to work at least one day next week, find the probability that she will be late less than three times.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Suzi will receive a bonus.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>35</mn><mo>,</mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>40</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>40</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>75</mn></math> <em><strong>(M1)</strong></em></p>
<p>attempt to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> graphically or numerically using the GDC <em><strong>(M1)</strong></em></p>
<p>graph of normal curve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>35</mn><mo>,</mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>40</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>40</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>75</mn></math><br>OR table of values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>40</mn></mrow></mfenced></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>40</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>413011</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>41</mn></math> (min) <em><strong>A2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>35</mn><mo>,</mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>40</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>40</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>75</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>674489</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p>valid equation using their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-score (clearly identified as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-score and not a probability) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>40</mn><mo>-</mo><mn>35</mn></mrow><mi>σ</mi></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>674489</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>674489</mn><mo>…</mo><mi>σ</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>413011</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>41</mn></math> (min) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>45</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>0886718</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>0887</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial probability <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>5</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>0886718</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>≥</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math> OR</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>≥</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>2</mn></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>3</mn></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>5</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>371400</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>≥</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>371</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing conditional probability in context <em><strong>(M1)</strong></em></p>
<p>finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mi>L</mi><mo><</mo><mn>3</mn></mrow></mfenced><mo>∩</mo><mfenced open="{" close="}"><mrow><mi>L</mi><mo>≥</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mfenced open="{" close="}"><mrow><mi>L</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>L</mi><mo>=</mo><mn>2</mn></mrow></mfenced></math> (may be seen in conditional probability) <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>L</mi><mo>=</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>36532</mn><mo>…</mo></math> (may be seen in conditional probability) <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mrow><mi>L</mi><mo><</mo><mn>3</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>L</mi><mo>≥</mo><mn>1</mn></menclose></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>36532</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>37140</mn><mo>…</mo></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>983636</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>984</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognizing that Suzi can be late no more than once (in the remaining six days) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>6</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>0886718</mn><mo>…</mo></mrow></mfenced></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> is the number of days late <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>1</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>907294</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mtext>Suzi gets a bonus</mtext></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>907</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> The first two marks may be awarded independently.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>recognizing that Suzi must be on time at least five times (of the remaining six days) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>6</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>911328</mn><mo>…</mo></mrow></mfenced></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> is the number of days on time <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>4</mn></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>0927052</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>5</mn></mrow></mfenced><mtext>+</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>6</mn></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>334434</mn><mo>…</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>572860</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>907294</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mtext>Suzi gets a bonus</mtext></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>907</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> The first two marks may be awarded independently.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates did not know to use inverse normal to find a <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math> value. Some did find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>, then rounded it to 3 sf and got an incorrect value for sigma.</p>
<p>Part (b) was mostly well done.</p>
<p>In (c) most recognised the binomial and handled 'at least one' correctly.</p>
<p>In (d) many recognised conditional probability, but most candidates were not able to find the intersection of the events as P(1) + P(2).</p>
<p>In part (e), those candidates who did understand what to do often misunderstood that they needed to look at 1 or no more lates and just considered one more late. Something similar happened to those who approached the question by considering the times Suzi was on time. </p>
<p>This question was only correctly answered by a few, and students tended to perform either very well or very poorly.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows values of ln <em>x</em> and ln <em>y</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between ln <em>x</em> and ln <em>y</em> can be modelled by the regression equation ln <em>y</em> = <em>a</em> ln <em>x</em> + <em>b</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the value of <em>y</em> when<em> x</em> = 3.57.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The relationship between <em>x</em> and <em>y</em> can be modelled using the formula <em>y</em> = <em>kx<sup>n</sup></em>, where <em>k</em> ≠ 0 , <em>n</em> ≠ 0 , <em>n</em> ≠ 1.</p>
<p>By expressing ln <em>y</em> in terms of ln <em>x</em>, find the value of <em>n</em> and of <em>k</em>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> one correct value</p>
<p>−0.453620, 6.14210</p>
<p><em>a</em> = −0.454, <em>b</em> = 6.14 <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution <em><strong> (A1)</strong></em></p>
<p><em>eg </em>−0.454 ln 3.57 + 6.14</p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em> ln <em>y</em> = 5.56484</p>
<p>261.083 (260.409 from 3 sf)</p>
<p><em>y</em> = 261, (<em>y</em> = 260 from 3sf) <em><strong>A1 N3</strong></em></p>
<p><strong>Note:</strong> If no working shown, award <em><strong>N1</strong></em> for 5.56484.<br>If no working shown, award <em><strong>N2</strong> </em>for ln <em>y</em> = 5.56484.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach for expressing ln <em>y</em> in terms of ln <em>x</em> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = {\text{ln}}\,\left( {k{x^n}} \right),\,\,{\text{ln}}\,\left( {k{x^n}} \right) = a\,{\text{ln}}\,x + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct application of addition rule for logs <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k + {\text{ln}}\,\left( {{x^n}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of exponent rule for logs <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k + n\,{\text{ln}}\,x">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>+</mo>
<mi>n</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span></p>
<p>comparing one term with regression equation (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = a,\,\,b = {\text{ln}}\,k">
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span></p>
<p>correct working for <em>k</em> <strong>(A1)</strong></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k = 6.14210,\,\,\,k = {e^{6.14210}}">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>6.14210</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mn>6.14210</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{{\text{ln}}\,y}} = {e^{a\,{\text{ln}}\,x + b}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct use of exponent laws for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{a\,{\text{ln}}\,x + b}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{a\,{\text{ln}}\,x}} \times {e^b}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</math></span></p>
<p>correct application of exponent rule for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\,{\text{ln}}\,x">
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,{x^a}">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</math></span></p>
<p>correct equation in<em> y</em> <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {x^a} \times {e^b}">
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</math></span></p>
<p>comparing one term with equation of model (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^b},\,\,n = a">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>valid approach for expressing ln <em>y</em> in terms of ln <em>x</em> (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = {\text{ln}}\,\left( {k{x^n}} \right),\,\,{\text{ln}}\,\left( {k{x^n}} \right) = a\,{\text{ln}}\,x + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct application of exponent rule for logs (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,\left( {{x^a}} \right) + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct working for <em>b</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = {\text{ln}}\,\left( {{e^b}} \right)">
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of addition rule for logs <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,\left( {{e^b}{x^a}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>comparing one term with equation of model (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^b},\,\,n = a">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In a group of 35 students, some take art class (<em>A</em>) and some take music class (<em>M</em>). 5 of these students do not take either class. This information is shown in the following Venn diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>One student from the group is chosen at random. Find the probability that</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of students in the group who take art class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the student does not take art class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the student takes either art class or music class, but not both.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {A \cap M'} \right) + \left( {A \cap M} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>M</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>M</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{17}}{{35}}">
<mfrac>
<mrow>
<mn>17</mn>
</mrow>
<mrow>
<mn>35</mn>
</mrow>
</mfrac>
</math></span>, 11 + 6</p>
<p>number of students taking art class = 17 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>13 + 5, 35 − 17, 18, 1 − P(<em>A</em>)</p>
<p>0.514285</p>
<p>P(<em>A'</em>) = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{18}}{{35}}">
<mfrac>
<mrow>
<mn>18</mn>
</mrow>
<mrow>
<mn>35</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.514 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>11 + 13, 35 − 6 − 5, 24</p>
<p>0.685714</p>
<p>P(<em>A</em> or <em>M</em> but not both) = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{24}}{{35}}">
<mfrac>
<mrow>
<mn>24</mn>
</mrow>
<mrow>
<mn>35</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.686 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The marks obtained by nine Mathematical Studies SL students in their projects (<em>x</em>) and their final IB examination scores (<em>y</em>) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The equation of the regression line <em>y</em> on <em>x</em> is <em>y</em> = <em>mx</em> + <em>c</em>.</p>
</div>
<div class="specification">
<p>A tenth student, Jerome, obtained a project mark of 17.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
<mrow>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean project mark.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean examination score.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <em>r </em>, Pearson’s product–moment correlation coefficient.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact value of <em>m</em> and of <em>c</em> for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the point M (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
<mrow>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>) lies on the regression line <em>y</em> on <em>x</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression line <em>y</em> on <em>x</em> to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In his final IB examination Jerome scored 65.</p>
<p>Calculate the percentage error in Jerome’s estimated examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>14 <em><strong>(G1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>54 <em><strong>(G1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.5 <em><strong>(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>m</em> = 0.875, <em>c</em> = 41.75 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {m = \frac{7}{8}{\text{,}}\,\,c = \frac{{167}}{4}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>167</mn>
</mrow>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 0.875 seen. Award <em><strong>(A1)</strong></em> for 41.75 seen. If 41.75 is rounded to 41.8 do not award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = 0.875(14) + 41.75 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into their regression line. Follow through from parts (a)(i) and (b)(i).</p>
<p> </p>
<p>= 54</p>
<p>and so the mean point lies on the regression line <em><strong>(A1)</strong></em></p>
<p>(accept 54 is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean value of the <em>y</em> data)</p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)</strong></em> unless the conclusion is explicitly stated and the 54 seen. The <em><strong>(A1)</strong></em> can be awarded only if their conclusion is consistent with their equation and it lies on the line.</p>
<p>The use of 41.8 as their <em>c</em> value precludes awarding <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>54 = 0.875(14) + 41.75 <em><strong>(M1)</strong></em></p>
<p>54 = 54</p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into their regression line. Follow through from parts (a)(i) and (b)(i).</p>
<p> </p>
<p>and so the mean point lies on the regression line <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)</strong></em> unless the conclusion is explicitly stated. Follow through from part (a). </p>
<p>The use of 41.8 as their <em>c</em> value precludes the awarding of <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = 0.875(17) + 41.75 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for correct substitution into their regression line.</p>
<p> </p>
<p>= 56.6 (56.625) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the estimate is valid <em><strong>(A1)</strong></em></p>
<p>since this is interpolation <strong>and</strong> the correlation coefficient is large enough <em><strong>(R1)</strong></em></p>
<p><strong>OR</strong></p>
<p>the estimate is not valid <em><strong>(A1)</strong></em></p>
<p>since the correlation coefficient is not large enough <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)(R0)</strong></em>. The <em><strong>(R1)</strong></em> may be awarded for reasoning based on strength of correlation, but do not accept “correlation coefficient is not strong enough” or “correlation is not large enough”.</p>
<p>Award <em><strong>(A0)</strong></em><em><strong>(R0)</strong></em> for this method if no numerical answer to part (a)(iii) is seen.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{56.6 - 65}}{{65}}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>56.6</mn>
<mo>−</mo>
<mn>65</mn>
</mrow>
<mrow>
<mn>65</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into percentage error formula. Follow through from part (c)(i).</p>
<p> </p>
<p>= 12.9 (%)(12.9230…) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (c)(i). Condone use of percentage symbol.<br>Award <em><strong>(G0)</strong></em> for an answer of −12.9 with no working.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Emlyn plays many games of basketball for his school team. The number of minutes he plays in each game follows a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> minutes.</p>
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn><mo> </mo><mtext>minutes</mtext></math>.</p>
</div>
<div class="specification">
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>minutes</mtext></math>.</p>
</div>
<div class="specification">
<p>The standard deviation of the number of minutes Emlyn plays in any game is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>.</p>
</div>
<div class="specification">
<p>There is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>%</mo></math> chance Emlyn plays less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> minutes in a game.</p>
</div>
<div class="specification">
<p>Emlyn will play in two basketball games today.</p>
</div>
<div class="specification">
<p>Emlyn and his teammate Johan each practise shooting the basketball multiple times from a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>. A record of their performance over the weekend is shown in the table below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>On Monday, Emlyn and Johan will practise and each will shoot <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math> times from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a diagram to represent this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>7</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability he plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in one game and more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in the other game.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of successful shots Emlyn will make on Monday, based on the results from Saturday and Sunday.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Emlyn claims the results from Saturday and Sunday show that his expected number of successful shots will be more than Johan’s.</p>
<p>Determine if Emlyn’s claim is correct. Justify your reasoning.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong><img 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GBuIMxLSkroo486iMFBEoJmuQXm5sacQY+KmkMhIcH04MED1UBzNygy43bA3CCY84K6w4cNEwMyzHDBU34SAubmx5wvgn71j39QWFhf4imazQiqP78TMDcA5jzwIiYmRjSvcHu5HEIzPAbm5secoeMpc9u2bUMzZ0ZiDVGF7QHmCieoGmfmvbm5VLduHVq5cqUpIeeTETC3BuZcP06cOCFmWNy+fRuicwX9AeYKJqYakF+9elVMaTtlyhTTQg7MrQO5VEdSUlIE6BcvXgDoChkEzBVKSKmQKnlbXl5OH3/8EQ0cOICOHDkCzHWcV0rmuxX2xdeAZs2cScFBgVRSXAzQFSjbwFyBRFSj8nFhH/bnBc99+/aZGnJE5taLzLnO8LqhX375hVirlsu7GvXISvsE5jrEnC94xsYuFhc8ecIiM1zgdPUd0GZuTdC5myJfEI2MnIELoj5aBMx9TEA1zvx79uwRU9omJCyzBOSIzK0JuVR3CgoKxAX+bdtwQVRKE29ugbnOMJfW8ORIxVU0a6bXEZlbG/SfUlOpXr16dO7sWTS3eGkSMPcy4bw5c7p6T1lZmZgFsX///qa/4Ck/EQFza2PObebTp08Tg+Lu3bsH0L1wCZh7kWiuUPbm9devX9OwYUNFYd6/33hreMpx9vQxMLc25lxneFrnr7763whRvu9NPbLye4C5DjB/+/Yt8RqePIGWWaa0BebA2RtYHz9+/OcaopMIPVw8K0PAXAeY78jMpIDatcWaiZ4iaJbtEZl7VnG9gdIo7+GBRLym7aZNmxCde+ATMPcgsdSoDGfPnhUj4TgyNwvM3nwPYA7MbetXVtZO0cPleAHWELVNF2f3gbkfMb9//76YEjQ8PNzwa3h6A7jte4A5MLeFisdazJ0bRc2aNaU7d24jQnfDKWDuRiLZFjKl7vMUoH36fEU9enSnQ4cOWToqZ9SBOTCX1603b97Qd9+NoK5dQ6mqqgqgu7AKmLtIIHkBU+IxX9iZMGECBQcHUVZWluUhB+aA3FG9qigvp66hoTR8+DDMge7CKmDuIoEcFTJfnl+/PkksocUXeGybGqx8H5E5QHdUp27cuEHNmzej+PiliM6deAXMnSSOo8Lly/O5OTlUq1ZNio+PB+THjlWnATAH5s7qFQc6vIbodgz5d3hCA+YaYs5drho2bECTJ02i/Pz8asisHJFL3x2YA3NnmPMF0S1bNoueXydPFhI/dra9FV8D5hph/vDhQ2rXri2Fhw8C4jYROTAH4p7AO2/uXAoKCqQ7d+4Ac5ldwFyWIJ4ULHe3ffr0qRimHNqlC3qu2IGcQUdkDtTdqU/cwyUiYjCFhnah0tJSgG7jFzC3SQx3CpOn23DhGz9+PLVq1ZKys7MRlQNzAORjneMVuBjzoUO/JZ7TyNM6adbtgbmPBctZweB2vUWLFol28rS0NEDuAHJE5ojKndUje68VFd0VXXtnzpyJ9vM/DQPmKmHOkHPXQ74Cv3LlSkDuBHJgDsztge3quZMnT4rFzteuXQPQ//jDU8vpL568w1VmmPn1Y8fyqU6dAIqOXgDIXUAOzIG5txbs3r1b1LPc3FzLN7d4YjNvC8zdiOS5C2K9eh/SxIkT0QXRDciBOTD3FnP+BbwxOVnUt8LCQkuDDszdwNmTglZUVCQWqB00cKDlVgtilL39R28WgO5JPbPdljsZzJkzmwIDWxGPFrV9zUr3gbmCmFdUVFC3bt3E5FmHDx/2GjZvQTTy+4A5MPcFXp7vaNSoUdSpU0cqfvTIkqADc4Uw51ndwsL6ioFBeXnWW/bN1xMJMAfmvmDO733+/LmYibR3715UVVVpOdCBuQKYc1QwZsxoatmyBe3cuQMRuRfNLcAcmPuKOb+/uLiYOnRoLwYWcfOLEvs0yj6AuQKYc3td06ZNKDU1FZB7ATlH9cAcmCuF5t27dykkJIQmT54MzJ0Ij94sNvi/ffsbrVixXFxJX7duHSD3EnJgDsiVglzaz5UrV6hZ0yY0b95cyywM7cRtuy8B8z8xf/v2LW3dmiL6uC5PSADkPkAOzIG5hLCStydOHBfriK5YsYK4viq5bz3uy67YTp4E5n9inrp1q1hBPDY2FpD7CDkwB+Zq4ci9yurWrUObN28C5jLYLY85D1LYtStLDNOPjo4G5ApADsyBuVqY834zMzP/XNlro6mH/cusdvnQ8pjn5x8VZ/qpU6didKdCkANzYK4m5rzv9LQ0ql+/Hu3Zs8e0oLvUW7aBpTE/fvy4mNhnwoTxgFxByIE5MFcbc97/Dz/8ICJ0Bl2L42l9DJnVLh9aFvOjR48KyHlucr7PAOFfuTRA10SArjZ+Yh6XjckC9CNHjpgOdJd6yzawJOac8bx255gxYwC5SicxYA7M1cac988D/GJjF1Ojhg2IL45qcUytjiGz2uVDy2Eumlbq16fRo0ejaUUlyNHMAsi1Ao+PwxF6XFyc+KXNU29oeWw1j+VSb9kGlsK8oKAATSsqAm7bTIXIHKCrCZ1839zvfP36JHFR9ODBg6a4KCqz2uVDy2Cek5MDyDWCHJE5IJdjq8VjbnJZs3q1aEPfsWOH4SN0l3rLNjA95vwTLCvrf/3IJ0+ehDZyjUBHZA7QtQBcfgyu70lJSSJw27gx2dAjRWVWu3xoasz5p1dKyo/iTB0ZOQNt5BpBjsgckMuR1fIxg56ZmSHGj/zww3rDzuXiUm/ZBqbFnDM0IWEZBdSuRYsXLwbkGkIOzIG5lng7Ota+fXsF6PPnzzNkG7rMapcPTYk5t53NnBkpZj9cvhyTZtlemNTqPppZALojZLV8nkd4N2/ejCZOmECvX782VDu6S71lG5gO8ydPntCIEcOpSZPGtH79egwE0jgil04WwByYa4m2s2NdvvyLWMf3m2/6U2lpqWFAl1nt8qGpML9//75YrzM4OIi2bUsH5H6CHM0sgNwZrv547d69e9SzZw/69NNP6Pbt24YA3aXesg1Mg/nZM2eobZs21LVrqJh8R4oQcavcEH1P0hKROUD3B9rOjllRUU7Dhg2loKBAKig4pnvQZVa7fGh4zPlC5/bt28Xw/CFDIoiH6nuCDrZVB3tgDsydweqv1/h62oL588X1tC1btui666JLvWUbGBrzZ8+e0ZLYWLGoRGRkJBD3Y7OK/KQIzIG5v8B257i8vi9PoTt79iyqrKzUZZQus9rlQ8Ni/vjxY+r79dfiQmdS0jp0PdQR5Aw7MAfm7qDqr234F/2FCxeoXbu21KvX58TX2/g5f30ee8d1qbdsA0NifvDAAdHuxe3jPGxXHhXisTpNJ56kKzAH5vaA0ttzJSXF9O23Q6hFi+aUnZ0NzLXKIG5W4QFAAQG1xayHPOWlJ8BgW+2QB+bAXCsXfD3OmzdvxABDXls0KmqObppdZIG3y4eGiMz558/Vq1dF1yIeAJCYmIhmFZ01q8hPlMAcmPuKrJbvZ2POnDktml24++LFixf93uziUm/ZBrrHnM+aS5fGiflVuNP/nj27EY3rHHKGHZgDcy0xVupYZWVlNH36NOFNTEwMvXr1ym9NLzKrXT7UNeYnThynzz/vKS5yLlmyBNG4ARCXInRgDsyVAlbr/fAEffv376c2bVpTly6fiRWM/HFx1KXesg10ifmjRw9pzpzZom18wIABtHdvLqJxA0GOyByQaw2wGserqqqiGTOmU506ATRlyr9Fjxc1juNonzKrXT7UFeZ8gZPnU+F5Vdq3b0cbNvyAaNxgiCMyB+SOcDLi8xyRcxfGnj16UMMG9WnVqlXEyGvxXVzqLdtAF5jzqKzNmzdRhw4dqGnTJrRw4ULipZ8kGHCrXS8UpdIazSxAXQvwtDoGz7jIi9xwv/S2bdtQcnIy8fU8NY8vs9rlQ79izpF4SkoKde7cmRo1akiTJk2iffv2AXGDRuO2JwJgDszVhM5f++aofO3atWKcS+fOncSqRuyYGp/Hpd6yDfyCeVHRXVq7do3oqN+0SRMaO3YMHThwAIibAHEJdGAOzNUATi/7fP78OfFaCRylN27ciFauXEE3b95UFHWZ1S4faoY5f3ke5DN4cLiYE4GnqY2OXoBI3ESAS5DzLTAH5nqBV83PwVE5T/THfdN5rpeBAwcI05SI1l3qLdtAVcxfvHghpqMdN3YshYQEi94pQ4cOpXXr1mF2Q5MiLoEOzIG5mojqbd983e/MmTM0Z/ZsMYMrB6ujR/+LMjIyiANZbz6vzGqXDxXDnC8Q3Lp1S8xvwH3CeYAPD7vnC5phYWFiGD733ZQqO26Nd1HTkzwD5sDcG8DM8B6OynnOqO+/n0itW4cIB8PC+tKiRYto586d9N///pdevnzpEniXess28Ajz27dv0e7d2fTjjz/Sxo3JtGjRQpowYbxY3admzRpUq1ZNatasKXXr1pXGjBkteqjw/OL5+flA3OSRuBx6YA7MzQCzL9+BuzXyAKRr165SbGysCHAZd54Dhr3s3r2b8JMd5W7Y7Cr7ykEx/3v65xHmO3Zkiknd+QPxyMzw8HAaO3YsxcREi6u6mZmZYuSUvGLjsbmjcHv5C8yBuS8QmvW93OTCS9idOnVKNMEsWRIrBiRFRAym/v37ibb3zMwM4n9P/zzCnBOYL2DyhO72KjCesx7ajvIcmANzs4Ks1fcC5hZrznCEqb+fB+bAXCv0zHocYA7MdfGrCZgDc7Miq9X3UhVzvkLboUN70V4+btw4wj/SwFEZ4OsqX331D+I2QfwjDVAG3C8DPKCS/z3986jNfOnSpaKrYadOHYlnM8Q/0kDPZYB/HdSo8QF9+eUXKKuor4YpA+PGjSX+9/TPI8z558Wvv/5KvJiyVj81cBz8XPe2DDx8+FDMwHn9+nWU1z9QjrwtR/56n+qY++uL4biojJ6WAWCOMuNpmdHT9sAcEQii0D/LADAH5nrC2dPPAsyBuWKY83zNPOeEo0LI6yM+ffrU4euO3mf7PM/fU1lZ6dM+bPdnex+YA3Pb8mC0+8AcmPsMIyOdl5dHXbuG0t27d9/bH88rMX/+PHFx8a9//T8xTPnOnTvvbeeo8vAJgmfQnDTpe5o2bSplZe10+72O9mnveWAOzO2VC6M8B8yBuU8wMuS7d++mgQMHEkMtx5znm5g3by6lpqaK+SN4+s+GDRtQv379xDwUrioKQz516hTq06cPMbautvfldWAOzH0pP/5+LzAH5ooAybO72cOc55a4dOnSO8dYsGA+BQa2Ip4501kFYMh5Jjme+9nX5hlnx5FeA+bAXCoLRrwF5sDcKajuFup9+/baxdze+1evTqTvvhtBHLXbe116bsuWLWKfe/fudbqdtL2vt3xyuXbtmlvTjfp6LLwfJw6lywAwB+aKQOku5gzmwpgYKisrc3pcvsgZFBhIoaFdqKyslI4ePSoWKFHr4qfSFQv7A9ZalwFgDsydoupugXSFOUfhPBhn0KCB1Lfv1++1rcuPw/Pa/+1vfxVNLPHxS4mj+RYtmlPHjh+LKUHl2+Mx8LR6GQDmwFwTzEtLS8Wcy6NGjRRIf/RRB+Juho4qIC8VyG3wvIyWtM2VK1fEKizDhw9z6+Kp9D7cAnorlAFgDsyrsfSlwLuKzKV9c4S+ePEiAXV6errDYy9cuJD+/ve/0blz56q34ffyhPzc/KLEArjSZ8ItsDdDGQDmwLwaS18KtLuY8zGqqqqoVs0aFBcX5/DYiYmJ9MEHf6cLFy68s01UVBQ1btxIk94tvqQH3osThNZlAJgD83ew9LYAeoI5H6NVq5ZUUFDg8Ni8WAa3mfM0yrafiZcc5K6Krro12r7H2f1Tp05SQkIC/XvyZBHtc3PQ1ClTaNasWaK3Df8aSE9PoxEjhr/XxdLZfvEaMNe6DABzYP4Olt4WQEeY8wK1Dx7cf+cYx48XUK9evd4Z+n/79m1as2YNVVRUiG25Pb17t270z3+Oqn4vw8qDk9auXVv9nLefV3pfSUkxjRgxgrp0+Yz4M0RGzhCPuYmHPwPPEx0fHy/WsmXgpffhFpB5lwsAAAJJSURBVFjrrQwAc2DuM1Dcfr1sWbxoB8/OziYeKCQV9LNnz4rnIyIiKCcnh1JTt9KwYUPp5s1fq7fhbXnFcb7gyauNS++9cf06hYQE04YNG8Toz02bNorVyaXXlbjlk03vXr1o+vRpxPPv84hWbtPv3LkTHTiwn44fPy5Qb9CgPqWk/Fj92ZQ4NvaBE4KSZQCYA3Ofgbp8+bLoA37gwAHKzz8q5rCXCik3h+Tm5orVg1auXEmFhYV2B+XcKyoSEbd8pCfPhc+IJiUl0enTp4kn85L2rcRtcXExMdRjxowWfd8Zd17xiFc/z8jYLppadmVliV40paWYl1+JNMc+1DmJAXNgriiORquo+/PyxC+CPXv2iHTgNvP69eoJ3LlZh7/P+PHjRN94ht5o3w+fVx049ZiuwByYWxoonomR16mVpu7dtWuXwP3kyZMiXbjZhZt6Vq1aael00iNe+EzvnqiAOTC3LFKvXr4Uy8TxhVcJBr4Yyn3Zpai84Ngx0d/9/PlzxE0y0na4fRcSpIf/0wOYA3PLAnXmzBnRFs4jSxmjJ0+eCNwztm+vTpOoqDmiJ8vmzZuqo3fA5X+4kAfv5wEwB+bVcFmtgty6dYu4943UZ527RWZmZlJ5eXl1mjD43IvG2dQDVks3fN/3IdVDmgBzYF4Nlx4KJD6DPqFAvug/X4A5MAfmKAMoAyYoA8DcBJmIqEn/URPyCHmkdhkA5sAcURnKAMqACcoAMDdBJqp9xsf+EVWiDOi/DABzYI6oDGUAZcAEZcBTzP8fHQ3C403Z17IAAAAASUVORK5CYII="> </strong> <strong><em>(A1)(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for bell shaped curve with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> <strong>or</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn></math> indicated. Award <em><strong>(A1)</strong></em> for approximately correct shaded region.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation using <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn></math> <strong>OR</strong> correctly shaded diagram indicating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn></math>. Strict or weak inequalities are accepted in parts (b), (c) and (d).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow><mn>2</mn></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M0)(M1)</strong></em> for unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow><mn>2</mn></mfrac></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <strong>OR</strong> the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn></math>. <br>Award at most <em><strong>(M1)(M0)</strong></em> if the final answer is not seen. Award <em><strong>(M0)(M0)</strong></em> for using known values <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>7</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>4</mn></math> to validate <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn></math><strong> </strong> <strong><em>(AG)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>13</mn><mo>≤</mo><mi>T</mi><mo>≤</mo><mn>18</mn></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation <strong>OR</strong> correctly shaded diagram indicating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math>.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>468</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>46</mn><mo>.</mo><mn>8</mn><mo>%</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>≥</mo><mn>20</mn></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation <strong>OR</strong> correctly shaded diagram indicating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math>.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>141</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>14</mn><mo>.</mo><mn>1</mn><mo>%</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mi>t</mi></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation <strong>OR</strong> for a correctly shaded region with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> indicated to the right-hand side of the mean.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>.</mo><mn>7</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>16</mn><mo>.</mo><mn>7133</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo><mo>×</mo><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo><mo>×</mo><mn>2</mn></math><strong> </strong> <strong><em>(M1)(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo><mo>×</mo><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo><mo>×</mo><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(M1)(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for the multiplication of their parts (c)(i) and (c)(ii), <em><strong>(M1)</strong></em> for multiplying their product by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> or for adding their products twice. Follow through from part (c).</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>132</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>13</mn><mo>.</mo><mn>2</mn><mo>%</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>132014</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(G0)</strong></em> for an unsupported final answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>066007</mn><mo>…</mo></math></p>
<p><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>69</mn><mn>102</mn></mfrac><mo>×</mo><mn>200</mn></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability multiplied by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math>.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>135</mn><mo>.</mo><mn>294</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)</em><em>(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>67</mn><mn>98</mn></mfrac><mo>×</mo><mn>200</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>136</mn><mo>.</mo><mn>734</mn><mo>…</mo></math><strong> </strong> <strong><em>(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>137</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>136</mn><mo>.</mo><mn>734</mn><mo>…</mo></math> seen.</p>
<p><br>Emlyn is incorrect,<strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo><</mo><mn>137</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>135</mn><mo>.</mo><mn>294</mn><mo>…</mo><mo><</mo><mn>136</mn><mo>.</mo><mn>734</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(R1)</em></strong></p>
<p><strong><br>Note:</strong> To award the final <em><strong>(R1)</strong></em>, both the conclusion and the comparison must be seen. Award at most <em><strong>(A0)(R1)</strong></em><strong>(ft)</strong> for consistent incorrect methods in parts (f) and (g).</p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>67</mn><mn>98</mn></mfrac><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>684</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>683673</mn><mo>…</mo></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>69</mn><mn>102</mn></mfrac><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>676</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>676470</mn><mo>…</mo></mrow></mfenced></math><strong> </strong> <strong><em>(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for both correct probabilities seen.</p>
<p><br>Emlyn is incorrect,<strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>676</mn><mo><</mo><mn>0</mn><mo>.</mo><mn>684</mn></math> </strong> <strong><em>(R1)</em></strong></p>
<p><strong><br>Note:</strong> To award the final <em><strong>(R1)</strong></em>, both the conclusion and the comparison must be seen. Award at most <em><strong>(A0)(R1)</strong></em><strong>(ft)</strong> for consistent incorrect methods in parts (f) and (g).</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>On a school excursion, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> students visited an amusement park. The amusement park’s main attractions are rollercoasters (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">R</mtext></math>), water slides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">W</mtext></math>), and virtual reality rides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">V</mtext></math>).</p>
<p>The students were asked which main attractions they visited. The results are shown in the Venn diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> students visited the rollercoasters or the water slides.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students who visited at least two types of main attraction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo> </mo><mi>R</mi><mo>∩</mo><mi>W</mi><mo>)</mo><mo> </mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the rollercoasters.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the virtual reality rides.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence determine whether the events in <strong>parts (d)(i)</strong> and <strong>(d)(ii)</strong> are independent. Justify your reasoning. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn><mo>-</mo><mfenced><mrow><mn>32</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>5</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn><mo>-</mo><mn>68</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br></strong><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up a correct expression.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>6</mn></math> <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mfenced><mrow><mn>74</mn><mo>+</mo><mn>18</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mn>92</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mfenced><mrow><mn>32</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>18</mn><mo>+</mo><mn>6</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up a correct expression. Follow through from part (a)(i) but only for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>b</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>8</mn></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong><br>Note:</strong> Follow through from part(a)(i). The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> must be greater or equal to zero for the <em><strong>(A1)</strong></em><strong>(ft)</strong> to be awarded.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for adding <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>,</mo><mo> </mo><mn>12</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>58</mn><mn>100</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>29</mn><mn>50</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>58</mn><mo>,</mo><mo> </mo><mn>58</mn><mo>%</mo></mrow></mfenced></math> <em><strong>(A1)(A1)(G2)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator. Award<em><strong>(A1)</strong></em> for the correct denominator. Award <em><strong>(A0)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn></math> only.</p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>45</mn><mn>100</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>9</mn><mn>20</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>,</mo><mo> </mo><mn>45</mn><mo>%</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Follow through from their denominator from part (d)(i).</p>
<p><em><strong><br></strong></em><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>they are not independent <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>58</mn><mn>100</mn></mfrac><mo>×</mo><mfrac><mn>45</mn><mn>100</mn></mfrac><mo>≠</mo><mfrac><mn>17</mn><mn>100</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>261</mn><mo>≠</mo><mn>0</mn><mo>.</mo><mn>17</mn></math> <em><strong>(R1)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Comparison of numerical values must be seen for <em><strong>(R1)</strong></em> to be awarded.<br>Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from parts (d)(i) and (d)(ii).</p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>At a school, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>%</mo></math> of the students play a sport and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>%</mo></math> of the students are involved in theatre. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>%</mo></math> of the students do neither activity.</p>
<p>A student is selected at random.</p>
</div>
<div class="specification">
<p>At the school <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn><mo>%</mo></math> of the students are girls, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math> of the girls are involved in theatre.</p>
<p>A student is selected at random. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> be the event “the student is a girl” and let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> be the event “the student is involved in theatre”.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student plays a sport and is involved in theatre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student is involved in theatre, but does not play a sport.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>G</mi><mo>∩</mo><mi>T</mi></mrow></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine if the events <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> are independent. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>S</mi></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mi>T</mi></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>'</mo><mo>∩</mo><mi>T</mi><mo>'</mo></mrow></mfenced><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>∩</mo><mi>T</mi></mrow></mfenced><mo>=</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>∪</mo><mi>T</mi></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mfenced><mrow><mi>S</mi><mo>'</mo><mo>∩</mo><mi>T</mi><mo>'</mo></mrow></mfenced><mi mathvariant="normal">'</mi></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>7</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>18</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>∩</mo><mi>T</mi></mrow></mfenced><mo>=</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>∪</mo><mi>T</mi></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>18</mn></math></p>
<p><br><strong>OR</strong></p>
<p>a clearly labelled Venn diagram <em><strong>(M1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mrow><mi>S</mi><mo>∩</mo><mi>T</mi></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>08</mn></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>%</mo></math>) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> To obtain the <em><strong>M1</strong></em> for the Venn diagram all labels must be correct and in the correct sections. For example, do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>7</mn></math> in the area corresponding to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>∩</mo><mi>T</mi><mo>'</mo></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>∩</mo><mi>S</mi><mo>'</mo></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mi>T</mi></mfenced><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>∩</mo><mi>S</mi></mrow></mfenced><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>08</mn></mrow></mfenced></math> OR</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>∩</mo><mi>S</mi><mo>'</mo></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>∪</mo><mi>S</mi></mrow></mfenced><mo>-</mo><mtext>P</mtext><mfenced><mi>S</mi></mfenced><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>82</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>7</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p> <br><strong>OR</strong></p>
<p>a clearly labelled Venn diagram including <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>S</mi></mfenced></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>T</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>∩</mo><mi>T</mi></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>12</mn></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>%</mo></math>) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>G</mi><mo>∩</mo><mi>T</mi></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>/</mo><mi>G</mi></mrow></mfenced><mtext>P</mtext><mfenced><mi>G</mi></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>48</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>12</mn></math> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>G</mi></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mi>T</mi></mfenced><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>48</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>096</mn></math><strong> <em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>G</mi></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mi>T</mi></mfenced><mi mathvariant="normal">≠</mi><mtext>P</mtext><mfenced><mrow><mi>G</mi><mo>∩</mo><mi>T</mi></mrow></mfenced><mi mathvariant="normal">⇒</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> are not independent<strong> <em>R1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo> </mo><menclose notation="left"><mo> </mo><mi>G</mi></menclose></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></math><strong> <em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo> </mo><menclose notation="left"><mo> </mo><mi>G</mi></menclose></mrow></mfenced><mo>≠</mo><mtext>P</mtext><mfenced><mi>T</mi></mfenced><mi mathvariant="normal">⇒</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> are not independent<strong> <em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <em><strong>A0R1</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The heights of adult males in a country are normally distributed with a mean of 180 cm and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma {\text{ cm}}">
<mi>σ</mi>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>. 17% of these men are shorter than 168 cm. 80% of them have heights between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(192 - h){\text{ cm}}">
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span> and 192 cm.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>finding the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</mi>
</math></span>-value for 0.17 <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = - 0.95416">
<mi>z</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.95416</mn>
</math></span></p>
<p>setting up equation to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span><em>, <strong>(M1)</strong></em></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = \frac{{168 - 180}}{\sigma },{\text{ }} - 0.954 = \frac{{ - 12}}{\sigma }">
<mi>z</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>168</mn>
<mo>−</mo>
<mn>180</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>0.954</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>12</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = 12.5765">
<mi>σ</mi>
<mo>=</mo>
<mn>12.5765</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong>EITHER (Properties of the Normal curve)</strong></p>
<p>correct value (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 192) = 0.83,{\text{ P}}(X > 192) = 0.17">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.83</mn>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.17</mn>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 192 - h) = 0.83 - 0.8,{\text{ P}}(X < 192 - h) = 1 - 0.8 - 0.17,">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.83</mn>
<mo>−</mo>
<mn>0.8</mn>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mn>0.8</mn>
<mo>−</mo>
<mn>0.17</mn>
<mo>,</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X > 192 - h) = 0.8 + 0.17">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.8</mn>
<mo>+</mo>
<mn>0.17</mn>
</math></span></p>
<p>correct equation in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{(192 - h) - 180}}{{12.576}} = - 1.88079,{\text{ }}192 - h = 156.346">
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>180</mn>
</mrow>
<mrow>
<mn>12.576</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>1.88079</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo>=</mo>
<mn>156.346</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p>35.6536</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 35.7">
<mi>h</mi>
<mo>=</mo>
<mn>35.7</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong>OR (Trial and error using different values of <em>h</em>)</strong></p>
<p><strong>two</strong> correct probabilities whose 2 sf will round up <strong>and</strong> down, respectively, to 0.8 <strong><em>A2</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(192 - 35.6 < X < 192) = 0.799706,{\text{ P}}(157 < X < 192) = 0.796284,">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mn>35.6</mn>
<mo><</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.799706</mn>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>157</mn>
<mo><</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.796284</mn>
<mo>,</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(192 - 36 < X < 192) = 0.801824">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mn>36</mn>
<mo><</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.801824</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 35.7">
<mi>h</mi>
<mo>=</mo>
<mn>35.7</mn>
</math></span> <strong><em>A2</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The following table shows the average body weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, and the average weight of the brain, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, of seven species of mammal. Both measured in kilograms (kg).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_10.57.27.png" alt="M17/5/MATSD/SP2/ENG/TZ1/01"></p>
</div>
<div class="specification">
<p>The average body weight of grey wolves is 36 kg.</p>
</div>
<div class="specification">
<p>In fact, the average weight of the brain of grey wolves is 0.120 kg.</p>
</div>
<div class="specification">
<p>The average body weight of mice is 0.023 kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of the average body weights for these seven species of mammal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the data from these seven species calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your regression line to estimate the average weight of the brain of grey wolves.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in your estimate in part (d).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether it is valid to use the regression line to estimate the average weight of the brain of mice. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="529 - 3">
<mn>529</mn>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 526{\text{ (kg)}}">
<mo>=</mo>
<mn>526</mn>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.922{\text{ }}(0.921857 \ldots )">
<mn>0.922</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.921857</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(very) strong, positive <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0.000986x + 0.0923{\text{ }}(y = 0.000985837 \ldots x + 0.0923391…)">
<mi>y</mi>
<mo>=</mo>
<mn>0.000986</mn>
<mi>x</mi>
<mo>+</mo>
<mn>0.0923</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mn>0.000985837</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>0.0923391</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.000986x">
<mn>0.000986</mn>
<mi>x</mi>
</math></span>, <strong><em>(A1) </em></strong>for 0.0923.</p>
<p>Award a maximum of <strong><em>(A1)(A0) </em></strong>if the answer is not an equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.000985837 \ldots (36) + 0.0923391 \ldots ">
<mn>0.000985837</mn>
<mo>…</mo>
<mo stretchy="false">(</mo>
<mn>36</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>0.0923391</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting 36 into their equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.128{\text{ (kg) }}\left( {0.127829 \ldots {\text{ (kg)}}} \right)">
<mn>0.128</mn>
<mrow>
<mtext> (kg) </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.127829</mn>
<mo>…</mo>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(</em></strong><strong><em>A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (c). The final <strong><em>(A1) </em></strong>is awarded only if their answer is positive.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{0.127829 \ldots - 0.120}}{{0.120}}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>0.127829</mn>
<mo>…</mo>
<mo>−</mo>
<mn>0.120</mn>
</mrow>
<mrow>
<mn>0.120</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into percentage error formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6.52{\text{ }}(\% ){\text{ }}\left( {6.52442...{\text{ }}(\% )} \right)">
<mn>6.52</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6.52442...</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (d). Do not accept a negative answer.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Not valid <strong><em>(A1)</em></strong></p>
<p>the mouse is smaller/lighter/weighs less than the cat (lightest mammal) <strong><em>(R1)</em></strong></p>
<p><strong><em>OR</em></strong></p>
<p>as it would mean the mouse’s brain is heavier than the whole mouse <strong><em>(R1)</em></strong></p>
<p><strong><em>OR</em></strong></p>
<p>0.023 kg is outside the given data range. <strong><em>(R1)</em></strong></p>
<p><strong><em>OR</em></strong></p>
<p>Extrapolation <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>(A1)(R0)</em></strong>. Do not accept percentage error as a reason for validity.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>At Penna Airport the probability, P(<em>A</em>), that all passengers arrive on time for a flight is 0.70. The probability, P(<em>D</em>), that a flight departs on time is 0.85. The probability that all passengers arrive on time for a flight and it departs on time is 0.65.</p>
</div>
<div class="specification">
<p>The number of hours that pilots fly per week is normally distributed with a mean of 25 hours and a standard deviation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ<!-- σ --></mi>
</math></span>. 90 % of pilots fly less than 28 hours in a week.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that event <em>A</em> and event <em>D</em> are <strong>not</strong> independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A \cap D'} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> Given that all passengers for a flight arrive on time, find the probability that the flight does <strong>not</strong> depart on time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>All flights have two pilots. Find the percentage of flights where <strong>both</strong> pilots flew more than 30 hours last week.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1</strong></p>
<p>multiplication of P(<em>A</em>) and P(<em>D</em>) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.70 × 0.85, 0.595</p>
<p>correct reasoning for their probabilities <em><strong>R1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.595 \ne 0.65">
<mn>0.595</mn>
<mo>≠</mo>
<mn>0.65</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.70 \times 0.85 \ne {\text{P}}\left( {A \cap D} \right)">
<mn>0.70</mn>
<mo>×</mo>
<mn>0.85</mn>
<mo>≠</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>D</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em>A</em> and <em>D</em> are not independent <em><strong>AG N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>calculation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {D\left| A \right.} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>D</mi>
<mrow>
<mo>|</mo>
<mi>A</mi>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{13}}{{14}}">
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
</math></span>, 0.928</p>
<p>correct reasoning for their probabilities <em><strong>R1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.928 \ne 0.85">
<mn>0.928</mn>
<mo>≠</mo>
<mn>0.85</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.65}}{{0.7}}{\text{P}}\left( D \right)">
<mfrac>
<mrow>
<mn>0.65</mn>
</mrow>
<mrow>
<mn>0.7</mn>
</mrow>
</mfrac>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>D</mi>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em>A</em> and <em>D</em> are not independent <em><strong>AG N0</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span style="background-color: #ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( A \right) - {\text{P}}\left( {A \cap D} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>D</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span> , 0.7 − 0.65 , correct shading and/or value on Venn diagram</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A \cap D'} \right) = 0.05">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.05</mn>
</math></span> <em><strong>A1 N2</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">recognizing conditional probability (seen anywhere) <strong><em><span style="font-family: 'Verdana',sans-serif;">(M1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg</span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}\left( {D' \cap A} \right)}}{{{\text{P}}\left( A \right)}}">
<mfrac>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
<mo>∩</mo>
<mi>A</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A\left| B \right.} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mrow>
<mo>|</mo>
<mi>B</mi>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working <strong><em><span style="font-family: 'Verdana',sans-serif;">(A1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg</span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.05}}{{0.7}}">
<mfrac>
<mrow>
<mn>0.05</mn>
</mrow>
<mrow>
<mn>0.7</mn>
</mrow>
</mfrac>
</math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">0.071428</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {D'\left| A \right.} \right) = \frac{1}{{14}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>|</mo>
<mi>A</mi>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
</math></span> , 0.0714 <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding standardized value for 28 hours (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = 1.28155">
<mi>z</mi>
<mo>=</mo>
<mn>1.28155</mn>
</math></span></p>
<p style="text-align: start;"><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">correct working to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span> <em><strong>(A1)</strong></em><br></span></p>
<p style="text-align: start;"><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.28155 = \frac{{28 - 25}}{\sigma }">
<mn>1.28155</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>28</mn>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{28 - 25}}{{1.28155}}">
<mfrac>
<mrow>
<mn>28</mn>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mrow>
<mn>1.28155</mn>
</mrow>
</mfrac>
</math></span></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.34091</span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = 2.34">
<mi>σ</mi>
<mo>=</mo>
<mn>2.34</mn>
</math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X > 30} \right) = 0.0163429">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>></mo>
<mn>30</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0163429</mn>
</math></span> <em><strong>(A1)</strong></em></p>
<p>valid approach (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left[ {{\text{P}}\left( {X > 30} \right)} \right]^2}">
<mrow>
<msup>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>></mo>
<mn>30</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span> , (0.01634)<sup>2</sup> , B(2, 0.0163429) , 2.67E-4 , 2.66E-4</p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">0.0267090</span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">0.0267 % <strong><em><span style="font-family: 'Verdana',sans-serif;">A2 N3</span></em></strong></span></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[4 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The table below shows the distribution of test grades for 50 IB students at Greendale School.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.25.22.png" alt="M17/5/MATSD/SP2/ENG/TZ1/05"></p>
</div>
<div class="specification">
<p>A student is chosen at random from these 50 students.</p>
</div>
<div class="specification">
<p>A second student is chosen at random from these 50 students.</p>
</div>
<div class="specification">
<p>The number of minutes that the 50 students spent preparing for the test was normally distributed with a mean of 105 minutes and a standard deviation of 20 minutes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mean test grade of the students;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the standard deviation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median test grade of the students.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student scored a grade 5 or higher.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of students that spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1(1) + 3(2) + 7(3) + 13(4) + 11(5) + 10(6) + 5(7)}}{{50}} = \frac{{230}}{{50}}">
<mfrac>
<mrow>
<mn>1</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>7</mn>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>13</mn>
<mo stretchy="false">(</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>11</mn>
<mo stretchy="false">(</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>10</mn>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>5</mn>
<mo stretchy="false">(</mo>
<mn>7</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>230</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into mean formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.6">
<mo>=</mo>
<mn>4.6</mn>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.46{\text{ }}(1.45602 \ldots )">
<mn>1.46</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1.45602</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>5 <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 - 4">
<mn>6</mn>
<mo>−</mo>
<mn>4</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for 6 and 4 seen.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 2">
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{11 + 10 + 5}}{{50}}">
<mfrac>
<mrow>
<mn>11</mn>
<mo>+</mo>
<mn>10</mn>
<mo>+</mo>
<mn>5</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11 + 10 + 5">
<mn>11</mn>
<mo>+</mo>
<mn>10</mn>
<mo>+</mo>
<mn>5</mn>
</math></span> seen.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{26}}{{50}}{\text{ }}\left( {\frac{{13}}{{25}},{\text{ }}0.52,{\text{ }}52\% } \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>26</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>25</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.52</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>52</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{10}}{{{\text{their }}26}} \times \frac{9}{{49}}">
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>26</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{10}}{{{\text{their }}26}}">
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>26</mn>
</mrow>
</mfrac>
</math></span> seen, <strong><em>(M1) </em></strong>for multiplying their first probability by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{9}{{49}}">
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\frac{{10}}{{50}} \times \frac{9}{{49}}}}{{\frac{{26}}{{50}}}}">
<mfrac>
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</mrow>
<mrow>
<mfrac>
<mrow>
<mn>26</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{10}}{{50}} \times \frac{9}{{49}}}">
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</mrow>
</math></span> seen, <strong><em>(M1) </em></strong>for dividing their first probability by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{their }}26}}{{50}}">
<mfrac>
<mrow>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>26</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{45}}{{637}}{\text{ (}}0.0706,{\text{ }}0.0706436 \ldots ,{\text{ }}7.06436 \ldots \% )">
<mo>=</mo>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>637</mn>
</mrow>
</mfrac>
<mrow>
<mtext> (</mtext>
</mrow>
<mn>0.0706</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.0706436</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>7.06436</mn>
<mo>…</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X \geqslant 90)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>⩾</mo>
<mn>90</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><img src="images/Schermafbeelding_2017-08-16_om_15.40.38.png" alt="M17/5/MATSD/SP2/ENG/TZ1/05.f.i/M"> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for a diagram showing the correct shaded region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( > 0.5)">
<mo stretchy="false">(</mo>
<mo>></mo>
<mn>0.5</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.773{\text{ }}(0.773372 \ldots ){\text{ }}0.773{\text{ }}(0.773372 \ldots ,{\text{ }}77.3372 \ldots \% )">
<mn>0.773</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.773372</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.773</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.773372</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>77.3372</mn>
<mo>…</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.773372 \ldots \times 50">
<mn>0.773372</mn>
<mo>…</mo>
<mo>×</mo>
<mn>50</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 38.7{\text{ }}(38.6686 \ldots )">
<mo>=</mo>
<mn>38.7</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>38.6686</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (f)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p>For each student, the number of hours spent on social media (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>) and the number of IB Diploma points obtained (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>) are shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.43.52.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>Use your graphic display calculator to find</p>
</div>
<div class="specification">
<p>Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.</p>
<p>The equation of the regression line <em>y </em>on <em>x </em>for these ten female students is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="y = - \frac{2}{3}x + \frac{{125}}{3}.">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>.</mo>
</math></span></p>
<p>An eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and 2 cm to represent 10 points on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
<mrow>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of hours spent on social media;</p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of IB Diploma points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on your scatter diagram and label this point M.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient, for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for these eight male students.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line, from part (e), on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a reason why this estimate is not reliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-03-07_om_08.41.53.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01.a/M"> <strong><em>(A4)</em></strong></p>
<p> </p>
<p><strong>Notes</strong>: Award <strong><em>(A1) </em></strong>for correct scale and labelled axes.</p>
<p>Award <strong><em>(A3) </em></strong>for 7 or 8 points correctly plotted,</p>
<p><strong><em>(A2) </em></strong>for 5 or 6 points correctly plotted,</p>
<p><strong><em>(A1) </em></strong>for 3 or 4 points correctly plotted.</p>
<p>Award at most <strong><em>(A0)(A3) </em></strong>if axes reversed.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> sufficient for labelling.</p>
<p>If graph paper is not used, award <strong><em>(A0)</em></strong>.</p>
<p>If an inconsistent scale is used, award <strong><em>(A0)</em></strong><em>. </em>Candidates’ points should be read from this scale <strong>where possible </strong>and awarded accordingly.</p>
<p>A scale which is too small to be meaningful (ie mm instead of cm) earns <strong><em>(A0) </em></strong>for plotted points.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x = 21">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mn>21</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y = 31">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mn>31</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> correctly plotted on graph <strong><em>(A1)</em>(ft)</strong></p>
<p>this point labelled M <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (b)(i) and (b)(ii).</p>
<p>Only accept M for labelling.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.973{\text{ }}( - 0.973388 \ldots )">
<mo>−</mo>
<mn>0.973</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>0.973388</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(G1) </em></strong>for 0.973, without minus sign.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 0.761x + 47.0{\text{ }}(y = - 0.760638 \ldots x + 46.9734 \ldots )">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.761</mn>
<mi>x</mi>
<mo>+</mo>
<mn>47.0</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.760638</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>46.9734</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.761x">
<mo>−</mo>
<mn>0.761</mn>
<mi>x</mi>
</math></span> and <strong><em>(A1)</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + 47.0">
<mo>+</mo>
<mn>47.0</mn>
</math></span>. Award a maximum of <strong><em>(A1)(A0) </em></strong>if answer is not an equation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line on graph <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <strong>straight line </strong>that passes through their M, <strong><em>(A1)</em>(ft) </strong>for line (extrapolated if necessary) that passes through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}47.0)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>47.0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p>If M is not plotted or labelled, follow through from part (e).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - \frac{2}{3}(34) + \frac{{125}}{3}">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>34</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution.</p>
<p> </p>
<p>19 (points) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>extrapolation <strong><em>(R1)</em></strong></p>
<p><strong>OR</strong></p>
<p>34 hours is outside the given range of data <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Do not accept ‘outlier’.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer produces 1500 boxes of breakfast cereal every day.</p>
<p>The weights of these boxes are normally distributed with a mean of 502 grams and a standard deviation of 2 grams.</p>
</div>
<div class="specification">
<p>All boxes of cereal with a weight between 497.5 grams and 505 grams are sold. The manufacturer’s income from the sale of each box of cereal is $2.00.</p>
</div>
<div class="specification">
<p>The manufacturer recycles any box of cereal with a weight <strong>not </strong>between 497.5 grams and 505 grams. The manufacturer’s recycling cost is $0.16 per box.</p>
</div>
<div class="specification">
<p>A <strong>different </strong>manufacturer produces boxes of cereal with weights that are normally distributed with a mean of 350 grams and a standard deviation of 1.8 grams.</p>
<p>This manufacturer sells all boxes of cereal that are above a minimum weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<p>They sell 97% of the cereal boxes produced.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a diagram that shows this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the probability that a box of cereal, chosen at random, is sold.</p>
<p>(ii) Calculate the manufacturer’s expected daily income from these sales.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the manufacturer’s expected daily recycling cost.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-03-08_om_11.51.39.png" alt="N16/5/MATSD/SP2/ENG/TZ0/04.a/M"></p>
<p><strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for bell shape with mean of 502.</p>
<p>Award <strong><em>(A1) </em></strong>for an indication of standard deviation <em>eg </em>500 and 504.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.921{\text{ }}(0.920968 \ldots ,{\text{ }}92.0968 \ldots \% )">
<mn>0.921</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.920968</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>92.0968</mn>
<mo>…</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a diagram showing the correct shaded region.</p>
<p> </p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1500 \times 2 \times 0.920968 \ldots ">
<mn>1500</mn>
<mo>×</mo>
<mn>2</mn>
<mo>×</mo>
<mn>0.920968</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {\text{ }}(\$ ){\text{ }}2760{\text{ }}(2762.90 \ldots )">
<mo>=</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">$</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2760</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>2762.90</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from their answer to part (b)(i).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1500 \times 0.16 \times 0.079031 \ldots ">
<mn>1500</mn>
<mo>×</mo>
<mn>0.16</mn>
<mo>×</mo>
<mn>0.079031</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1500 \times 0.16 \times {\text{ their }}(1 - 0.920968 \ldots )">
<mn>1500</mn>
<mo>×</mo>
<mn>0.16</mn>
<mo>×</mo>
<mrow>
<mtext> their </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mn>0.920968</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1500 - 1381.45) \times 0.16">
<mo stretchy="false">(</mo>
<mn>1500</mn>
<mo>−</mo>
<mn>1381.45</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>0.16</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1500 - {\text{their }}1381.45) \times 0.16">
<mo stretchy="false">(</mo>
<mn>1500</mn>
<mo>−</mo>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>1381.45</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>0.16</mn>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = (\$ )19.0{\text{ (}}18.9676 \ldots )">
<mo>=</mo>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">$</mi>
<mo stretchy="false">)</mo>
<mn>19.0</mn>
<mrow>
<mtext> (</mtext>
</mrow>
<mn>18.9676</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="347{\text{ }}({\text{grams}}){\text{ }}(346.614 \ldots )">
<mn>347</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>grams</mtext>
</mrow>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>346.614</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(G2) </em></strong>for an answer that rounds to 346.</p>
<p>Award <strong><em>(G1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="353.385 \ldots ">
<mn>353.385</mn>
<mo>…</mo>
</math></span> seen without working (for finding the top 3%).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The final examination results obtained by a group of 3200 Biology students are summarized on the cumulative frequency graph.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>350 of the group obtained the highest possible grade in the examination.</p>
</div>
<div class="specification">
<p>The grouped frequency table summarizes the examination results of this group of students.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median of the examination results.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the final examination result required to obtain the highest possible grade.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the modal class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the mid-interval value of the modal class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate an estimate of the mean examination result.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate an estimate of the standard deviation, giving your answer correct to <strong>three decimal places</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The teacher sets a grade boundary that is one standard deviation below the mean.</p>
<p>Use the cumulative frequency graph to estimate the number of students whose final examination result was below this grade boundary.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>60 <em><strong> (A2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>68 − 48 <em><strong> (A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correct quartiles seen, <em><strong>(M1)</strong></em> for finding the difference between their two quartiles.</p>
<p> </p>
<p>= 20 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3200 − 350 = 2850 <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 2850 seen. Follow through from their 3200.</p>
<p> </p>
<p>(Top grade boundary =) 76 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>60 < <em>x</em> ≤ 80 <em><strong> (A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 60, 80 seen, <em><strong>(A1)</strong></em> for correct strict and weak inequalities.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>70 <em><strong> (A1)</strong></em><strong>(</strong><strong>ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c)(i).</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>57.2 (57.1875) <em><strong> (A2)</strong></em><strong>(</strong><strong>ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c)(ii).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>18.496 <em><strong> (A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> for 18.499.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>57.2 − 18.5 <em><strong> (M1)</strong></em></p>
<p>= 38.7 (38.6918…) <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their standard deviation from their mean. Follow through from part (d) even if no working is shown.</p>
<p> </p>
<p>450 (students) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Accept any answer within the range of 450 to 475, inclusive. Follow through from part (d), adjusting the acceptable range as necessary.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>
<div class="specification">
<p>A second person is chosen from the group.</p>
</div>
<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>
<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>
<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both people chosen are <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{34}}{{60}} \times \frac{{33}}{{59}}">
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>60</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>33</mn>
</mrow>
<mrow>
<mn>59</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct product.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.317{\text{ }}\left( {\frac{{187}}{{590}},{\text{ }}0.316949 \ldots ,{\text{ }}31.7\% } \right)">
<mo>=</mo>
<mn>0.317</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>187</mn>
</mrow>
<mrow>
<mn>590</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.316949</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>31.7</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-14_om_05.54.09.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c/M"> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of branches.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 0.006 by 0.98.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.00588{\text{ }}\left( {\frac{{147}}{{25000}},{\text{ }}0.588\% } \right)">
<mo>=</mo>
<mn>0.00588</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>147</mn>
</mrow>
<mrow>
<mn>25000</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.588</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98 + 0.994 \times 0.05{\text{ }}(0.00588 + 0.994 \times 0.05)">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.00588</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their two correct products, <strong><em>(M1) </em></strong>for adding two products.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.0556{\text{ }}\left( {0.05558,{\text{ }}5.56\% ,{\text{ }}\frac{{2779}}{{50000}}} \right)">
<mo>=</mo>
<mn>0.0556</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.05558</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5.56</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>2779</mn>
</mrow>
<mrow>
<mn>50000</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c) and (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.006 \times 0.98}}{{0.05558}}">
<mfrac>
<mrow>
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</mrow>
<mrow>
<mn>0.05558</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct numerator, <strong><em>(M1) </em></strong>for their correct denominator.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.106{\text{ }}\left( {0.105793 \ldots ,{\text{ }}10.6\% ,{\text{ }}\frac{{42}}{{397}}} \right)">
<mo>=</mo>
<mn>0.106</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.105793</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>10.6</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>397</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (d) and (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.105793 \ldots \times 38">
<mn>0.105793</mn>
<mo>…</mo>
<mo>×</mo>
<mn>38</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 38 by their answer to part (f).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.02{\text{ }}(4.02015 \ldots )">
<mo>=</mo>
<mn>4.02</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4.02015</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (f). Use of 3 sf result from part (f) results in an answer of 4.03 (4.028).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>There are 54 employees in the company.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = 0.2 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>b</em> = 0.85 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(M1)</strong></em> for a correct product.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)"> <mo>=</mo> <mn>0.2</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mspace width="thinmathspace"></mspace> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>20</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 + 0.75 × 0.15 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their (0.25 × 0.8) and (0.75 × 0.15), <em><strong>(M1)</strong></em> for adding two products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)"> <mo>=</mo> <mn>0.313</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.3125</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>5</mn> <mrow> <mn>16</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>31.3</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> only if answer does not exceed 1. Follow through from part (b)(i).</p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}"> <mfrac> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> </mrow> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> <mo>+</mo> <mn>0.75</mn> <mo>×</mo> <mn>0.15</mn> </mrow> </mfrac> </math></span> <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a correct numerator (their part (b)(i)), <strong><em>(A1)</em>(ft)</strong> for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)"> <mo>=</mo> <mn>0.64</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>64</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft)</strong> only if answer does not exceed 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>x</em> =) 3 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>y</em> =) 10 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Following through from part (c)(i) but only if their <em>x</em> is less than or equal to 13.</p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their correct sum from 54. Follow through from their part (c).</p>
<p>= 8 <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> only if their sum does not exceed 54. Follow through from their part (c).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 + 8 + 13 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award (M1) for summing 6, 8 and 13.</p>
<p>27 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Adam is a beekeeper who collected data about monthly honey production in his bee hives. The data for six of his hives is shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.46.13.png" alt="N17/5/MATME/SP2/ENG/TZ0/08"></p>
<p>The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = aN + b">
<mi>P</mi>
<mo>=</mo>
<mi>a</mi>
<mi>N</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>Adam has 200 hives in total. He collects data on the monthly honey production of all the hives. This data is shown in the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.49.33.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e"></p>
<p>Adam’s hives are labelled as low, regular or high production, as defined in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.51.25.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e_02"></p>
</div>
<div class="specification">
<p>Adam knows that 128 of his hives have a regular production.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this regression line to estimate the monthly honey production from a hive that has 270 bees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of low production hives.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>;</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of hives that have a high production.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of setup <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 6.96103,{\text{ }}b = - 454.805">
<mi>a</mi>
<mo>=</mo>
<mn>6.96103</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>454.805</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 6.96,{\text{ }}b = - 455{\text{ (accept }}6.96x - 455)">
<mi>a</mi>
<mo>=</mo>
<mn>6.96</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>455</mn>
<mrow>
<mtext> (accept </mtext>
</mrow>
<mn>6.96</mn>
<mi>x</mi>
<mo>−</mo>
<mn>455</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = 270">
<mi>N</mi>
<mo>=</mo>
<mn>270</mn>
</math></span> into <strong>their</strong> equation <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6.96(270) - 455">
<mn>6.96</mn>
<mo stretchy="false">(</mo>
<mn>270</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>455</mn>
</math></span></p>
<p>1424.67</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 1420{\text{ (g)}}">
<mi>P</mi>
<mo>=</mo>
<mn>1420</mn>
<mrow>
<mtext> (g)</mtext>
</mrow>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>40 (hives) <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="128 + 40">
<mn>128</mn>
<mo>+</mo>
<mn>40</mn>
</math></span></p>
<p>168 hives have a production less than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 1640">
<mi>k</mi>
<mo>=</mo>
<mn>1640</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="200 - 168">
<mn>200</mn>
<mo>−</mo>
<mn>168</mn>
</math></span></p>
<p>32 (hives) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognize binomial distribution (seen anywhere) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim {\text{B}}(n,{\text{ }}p),{\text{ }}\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{(1 - p)^{n - r}}">
<mi>X</mi>
<mo>∼</mo>
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>n</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mi>p</mi>
<mi>r</mi>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mi>p</mi>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct values <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 40">
<mi>n</mi>
<mo>=</mo>
<mn>40</mn>
</math></span> (check <em><strong>FT</strong></em>) and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.75">
<mi>p</mi>
<mo>=</mo>
<mn>0.75</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 30,{\text{ }}\left( {\begin{array}{*{20}{c}} {40} \\ {30} \end{array}} \right){0.75^{30}}{(1 - 0.75)^{10}}">
<mi>r</mi>
<mo>=</mo>
<mn>30</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>40</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>30</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mn>0.75</mn>
<mrow>
<mn>30</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mn>0.75</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>0.144364</p>
<p>0.144 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following frequency table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_09.52.57.png" alt="M17/5/MATME/SP2/ENG/TZ1/01"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the mode.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the variance.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{mode}} = 10">
<mrow>
<mtext>mode</mtext>
</mrow>
<mo>=</mo>
<mn>10</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x_{\max }} - {x_{\min }}">
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mo movablelimits="true" form="prefix">max</mo>
</mrow>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mo movablelimits="true" form="prefix">min</mo>
</mrow>
</msub>
</mrow>
</math></span>, interval 2 to 11</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{range}} = 9">
<mrow>
<mtext>range</mtext>
</mrow>
<mo>=</mo>
<mn>9</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>7.14666</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{mean}} = 7.15">
<mrow>
<mtext>mean</mtext>
</mrow>
<mo>=</mo>
<mn>7.15</mn>
</math></span> <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that variance is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({\text{sd}})^2}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>sd</mtext>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\operatorname{var} = {\sigma ^2},{\text{ 2.9060}}{{\text{5}}^2},{\text{ }}{2.92562^2}">
<mi>var</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>σ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> 2.9060</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>5</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mn>2.92562</mn>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2} = 8.44515">
<mrow>
<msup>
<mi>σ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>8.44515</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2} = 8.45">
<mrow>
<msup>
<mi>σ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>8.45</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, in grams, of oranges grown in an orchard, are normally distributed with a mean of 297 g. It is known that 79 % of the oranges weigh more than 289 g and 9.5 % of the oranges weigh more than 310 g.</p>
</div>
<div class="specification">
<p>The weights of the oranges have a standard deviation of σ.</p>
</div>
<div class="specification">
<p>The grocer at a local grocery store will buy the oranges whose weights exceed the 35th percentile.</p>
</div>
<div class="specification">
<p>The orchard packs oranges in boxes of 36.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that an orange weighs between 289 g and 310 g.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the standardized value for 289 g.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of σ.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>To the nearest gram, find the minimum weight of an orange that the grocer will buy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the grocer buys more than half the oranges in a box selected at random.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The grocer selects two boxes at random.</p>
<p>Find the probability that the grocer buys more than half the oranges in each box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>correct approach indicating subtraction <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.79 − 0.095, appropriate shading in diagram</p>
<p>P(289 < <em>w</em> < 310) = 0.695 (exact), 69.5 % <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>eg 1 − <em>p</em>, 21</p>
<p>−0.806421</p>
<p><em>z</em> = −0.806 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>(i) & (ii)</p>
<p>correct expression for <em>z</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{289 - u}}{\sigma }">
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mi>u</mi>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> 1 − <em>p</em>, 21</p>
<p>−0.806421</p>
<p><em>z</em> = −0.806 (seen anywhere) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to standardize <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = \frac{{289 - 297}}{z},\,\,\frac{{289 - 297}}{\sigma }">
<mi>σ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>z</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>correct substitution with their <em>z</em> (do not accept a probability) <em><strong>A1</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.806 = \frac{{289 - 297}}{\sigma },\,\,\frac{{289 - 297}}{{ - 0.806}}">
<mo>−</mo>
<mn>0.806</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.806</mn>
</mrow>
</mfrac>
</math></span></p>
<p>9.92037</p>
<p>σ = 9.92 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>(i) & (ii)</p>
<p>correct expression for <em>z</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{289 - u}}{\sigma }">
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mi>u</mi>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> 1 − <em>p</em>, 21</p>
<p>−0.806421</p>
<p><em>z</em> = −0.806 (seen anywhere) <em><strong>A1 N2</strong></em></p>
<p>valid attempt to set up an equation with <strong>their</strong> <em>z</em> (do not accept a probability) <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.806 = \frac{{289 - 297}}{\sigma },\,\,\frac{{289 - 297}}{{ - 0.806}}">
<mo>−</mo>
<mn>0.806</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.806</mn>
</mrow>
</mfrac>
</math></span></p>
<p>9.92037</p>
<p>σ = 9.92 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> P(<em>W</em> < <em>w</em>) = 0.35, −0.338520 (accept 0.385320), diagram showing values in a standard normal distribution</p>
<p>correct score at the 35th percentile <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 293.177</p>
<p>294 (g) <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> If working shown, award <em><strong>(M1)(A1)A0</strong></em> for 293.<br>If no working shown, award <em><strong>N1</strong></em> for 293.177, <em><strong>N1</strong></em> for 293.</p>
<p>Exception to the <em><strong>FT</strong> </em>rule: If the score is incorrect, and working shown, award <em><strong>A1FT</strong></em> for correctly finding their minimum weight (by rounding up)</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of recognizing binomial (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim {\text{B}}\left( {36,\,\,p} \right),\,\,{}_n{C_a} \times {p^a} \times {q^{n - a}}">
<mi>X</mi>
<mo>∼</mo>
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>36</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<msub>
<mrow>
</mrow>
<mi>n</mi>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mi>a</mi>
</msub>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>p</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>a</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct probability (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.65</p>
<p><strong>EITHER</strong></p>
<p>finding P(<em>X</em> ≤ 18) from GDC <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.045720</p>
<p>evidence of using complement <em><strong>(M1)</strong></em></p>
<p><em>eg</em> 1−P(<em>X</em> ≤ 18)</p>
<p>0.954279</p>
<p>P(<em>X</em> > 18) = 0.954 <em><strong>A1 N2</strong></em></p>
<p><strong>OR</strong></p>
<p>recognizing P(<em>X</em> > 18) = P(<em>X</em> ≥ 19) <em><strong>(M1)</strong></em></p>
<p>summing terms from 19 to 36 <em><strong>(A1)</strong></em></p>
<p><em>eg</em> P(<em>X</em> = 19) + P(<em>X</em> = 20) + … + P(<em>X</em> = 36)</p>
<p>0.954279</p>
<p>P(<em>X</em> > 18) = 0.954 <em><strong>A1 N2</strong></em></p>
<p><strong>[<em>5</em><em> marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct calculation <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{0.954^2},\,\,\left( \begin{gathered} 2 \hfill \\ 2 \hfill \\ \end{gathered} \right){0.954^2}{\left( {1 - 0.954} \right)^0}">
<mrow>
<msup>
<mn>0.954</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mn>0.954</mn>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.954</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>0</mn>
</msup>
</mrow>
</math></span></p>
<p>0.910650</p>
<p>0.911 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory manufactures lamps. It is known that the probability that a lamp is found to be defective is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>05</mn></math>. A random sample of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> lamps is tested.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that there is at least one defective lamp in the sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that there is at least one defective lamp in the sample, find the probability that there are at most two defective lamps.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>recognize that the variable has a Binomial distribution <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>30</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>05</mn></mrow></mfenced></math></p>
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>1</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><msup><mn>95</mn><mn>30</mn></msup></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>214638</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>785361</mn><mo>…</mo></math></p>
<p><br><strong>Note:</strong> The two <em><strong>M</strong></em> marks are independent of each other.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>1</mn></mrow></mfenced><mtext>=0.785</mtext></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of conditional probability <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>2</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>X</mi><mo>≥</mo><mn>1</mn></menclose></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mtext>at most 2 defective</mtext><mo> </mo><mo>|</mo><mo> </mo><mtext>at least 1 defective</mtext></mrow></mfenced></math></p>
<p><br><strong>Note:</strong> Recognition must be shown in context either in words or symbols but not just <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi></menclose></mrow></mfenced></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mn>1</mn><mo>≤</mo><mi>X</mi><mo>≤</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>1</mn></mrow></mfenced><mi mathvariant="normal">+</mi><mtext>P</mtext><mfenced><mrow><mi mathvariant="normal">X</mi><mo>=</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>597540</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>785361</mn><mo>…</mo></mrow></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>812178</mn><mo>…</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>214638</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>785361</mn><mo>…</mo></mrow></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>338903</mn><mo>…</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>258636</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>785361</mn><mo>…</mo></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>760847</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>2</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>X</mi><mo>≥</mo><mn>1</mn></menclose></mrow></mfenced><mtext> </mtext><mi mathvariant="normal">=</mi><mo> </mo><mn>0</mn><mo>.</mo><mn>761</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The weight, <em>W</em>, of basketball players in a tournament is found to be normally distributed with a mean of 65 kg and a standard deviation of 5 kg.</p>
</div>
<div class="specification">
<p>The probability that a basketball player has a weight that is within 1.5 standard deviations of the mean is <em>q</em>.</p>
</div>
<div class="specification">
<p>A basketball coach observed 60 of her players to determine whether their performance and their weight were independent of each other. Her observations were recorded as shown in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>She decided to conduct a <em>χ </em><sup>2</sup> test for independence at the 5% significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a basketball player has a weight that is less than 61 kg.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a training session there are 40 basketball players.</p>
<p>Find the expected number of players with a weight less than 61 kg in this training session.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a normal curve to represent this probability.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>q</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P(<em>W</em> > <em>k</em>) = 0.225 , find the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test state the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test find the<em> p</em>-value.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a conclusion for this test. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>P(<em>W</em> < 61) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability statement.</p>
<p><strong>OR</strong></p>
<p><img src="data:image/png;base64,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"> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct region labelled and shaded on diagram.</p>
<p>= 0.212 (0.21185…, 21.2%) <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>40 × 0.21185… <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for product of 40 and their 0.212.</p>
<p>= 8.47 (8.47421...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a)(i) provided their answer to part (a)(i) is less than 1.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><em><strong><img 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"> (A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correctly labelled vertical lines in approximately correct positions. The values 57.5 and 72.5, or <em>μ </em>− 1.5<em>σ</em> and <em>μ </em>+ 1.5<em>σ</em> are acceptable labels. Award <em><strong>(M1)</strong></em> for correctly shaded region marked by their two vertical lines.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.866 (0.86638…, 86.6%) <strong><em> (A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their part (b)(i) shaded region if their values are clear.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P(<em>W</em> < <em>k</em>) = 0.775 <strong><em> (M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> <em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct region labelled and shaded on diagram.</p>
<p>(<em>k</em> =) 68.8 (68.7770…) <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(H<sub>0</sub>:) performance (of players) and (their) weight are independent. <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “there is no association between performance (of players) and (their) weight”. Do not accept "not related" or "not correlated" or "not influenced".</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.287 (0.287436…) <em><strong>(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>accept/ do not reject null hypothesis/H<sub>0</sub> <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>performance (of players) and (their) weight are independent. <strong><em>(A1)</em>(ft)</strong></p>
<p>0.287 > 0.05 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Accept <em>p</em>-value>significance level provided their <em>p</em>-value is seen in b(ii). Accept 28.7% > 5%. Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from part (d).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span>, of newborn babies in Australia are normally distributed with a mean 3.41 kg and standard deviation 0.57 kg. A newborn baby has a low birth weight if it weighs less than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> kg.</p>
</div>
<div class="question">
<p>Given that 5.3% of newborn babies have a low birth weight, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = - 1.61643">
<mi>z</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1.61643</mn>
</math></span>, <img src="images/Schermafbeelding_2017-03-06_om_06.21.13.png" alt="N16/5/MATME/SP2/ENG/TZ0/05.a/M"></p>
<p>2.48863</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 2.49{\text{ (kg)}}">
<mi>w</mi>
<mo>=</mo>
<mn>2.49</mn>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.</p>
<p>A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.</p>
<p> </p>
<p style="padding-left: 240px;">Set <em>S</em> represents those students who are <strong>taught</strong> in Spanish.</p>
<p style="padding-left: 240px;">Set <em>B</em> represents those students who <strong>study</strong> Biology.</p>
<p style="padding-left: 240px;">Set <em>M</em> represents those students who <strong>study</strong> Mathematics.</p>
<p style="padding-left: 210px;"> </p>
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"></p>
</div>
<div class="specification">
<p>A student from the school is chosen at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that are taught in Spanish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study Mathematics in English.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study both Biology and Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {S \cap \left( {M \cup B} \right)} \right)">
<mi>n</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>S</mi>
<mo>∩</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>M</mi>
<mo>∪</mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {B \cap M \cap S'} \right)">
<mi>n</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>B</mi>
<mo>∩</mo>
<mi>M</mi>
<mo>∩</mo>
<msup>
<mi>S</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies neither Biology nor Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student is taught in Spanish, given that the student studies Biology.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>10 + 40 + 28 + 17 <em><strong>(M1)</strong></em></p>
<p>= 95 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>20 + 12 <em><strong>(M1)</strong></em></p>
<p>= 32 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 + 40 <em><strong>(M1)</strong></em></p>
<p>= 52 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>78 <em><strong>(A1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 <em><strong>(A1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{100}}{{160}}">
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{8}{\text{,}}\,\,0.625{\text{,}}\,\,62.5\,{\text{% }}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>8</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.625</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>62.5</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{42}}{{160}}">
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{21}}{{80}}{\text{,}}\,\,0.263\,\,\left( {0.2625} \right){\text{,}}\,\,26.3\,{\text{% }}\,\,\left( {26.25\,{\text{% }}} \right)} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>21</mn>
</mrow>
<mrow>
<mn>80</mn>
</mrow>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.263</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.2625</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>26.3</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>26.25</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{50}}{{70}}">
<mfrac>
<mrow>
<mn>50</mn>
</mrow>
<mrow>
<mn>70</mn>
</mrow>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{7}{\text{,}}\,\,0.714\,\,\left( {0.714285 \ldots } \right){\text{,}}\,\,71.4\,{\text{% }}\,\,\left( {71.4285 \ldots \,{\text{% }}} \right)} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>7</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.714</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.714285</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>71.4</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>71.4285</mn>
<mo>…</mo>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Lucy sells hot chocolate drinks at her snack bar and has noticed that she sells more hot chocolates on cooler days. On six different days, she records the maximum daily temperature, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, measured in degrees centigrade, and the number of hot chocolates sold, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math>. The results are shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmoAAABOCAYAAACQcDp2AAAgAElEQVR4Ae1dz2scSbLe/0QGnSQQ2Pjik09mkX0QxsxhwBcPssCG9eLDwAxIyOwwh8cYWowYWBhYJMYMLA/sFl6WBeOhmctgtDS8hWEQ/ZjDYESzmIcRzWKMaeIRWRlZUVlRv7qzW9VVIRBdXZWVGd8XUZFfZWZV/w70TxlQBpQBZUAZUAaUAWWglgz8rpZWqVHKgDKgDCgDyoAyoAwoA6BCTYNAGVAGlAFlQBlQBpSBmjKgQq2mjlGzlAFlQBlQBpQBZUAZSAi15aULoP/KgcaAxoDGgMaAxoDGgMbA+cUAl6cpocYP6rYyoAy0mwFM1G34U5zN87L6tFk+bbM/Vag1K5YVjTIQlIE2J8egRNaksrb4E+luC1bFWZOLK5AZkj9VqAUiV6tRBprIgJQ0FOfiMtAWf6KH2oJVcS7u9ShZLvlThZrElO5TBpQBw4CUNJpIjeJsnlfVp83yaZv9qUKtWbGsaJSBoAy0OTkGJbImlbXFn0h3W7AqzppcXIHMkPypQi0QuVqNMtBEBqSkoTgXl4G2+BM91BasinNxr0fJcsmfKtQkpnSfMqAMGAakpNFEahRn87yqPm2WT9vsTxVqzYplRaMMBGWgzckxKJE1qawt/kS624JVcdbk4gpkhuRPFWqByNVqlIEmMiAlDcW5uAy0xZ/oobZgVZyLez1Klkv+VKEmMaX7lAFlwDAgJY0mUqM4m+dV9WmzfNpmf6pQa1YsKxplICgDbU6OQYmsSWVt8SfS3RasirMmF1cgMyR/TifUhl3Ycr8Pegm2uq+Tpp71YGcl/q2sy50+fEiWmPLbBxh2H5gLcnmzC8Mpazu/08cwGvwIzzrbsN8fnZ8Z593yaAC9px3449eh42QaYG+h37kFy0u34XDwzlU0HhzATRf7cYzjRRb/X4Wd3huIyq7Cjc4xLJp3paThSAiycQaD3nN41rkLl7d7cFZQ5/i0C/dXkr4oOKXU4dnjLGVGXGg0gB86d2HNxtPa5j78MChiJz49a6t2OLmh49/g6N5VuHlwAmO+f8Lt2WKNcvbR0w5sXdyF3plk8RkMXu7DFvWBK3dh7+UgeA6YLU4AwLzc/SvsbW6YfCa5Yzz8CfY3r0S5b30XjgLEqt/OzHH6DRbirpa7/Oqzvks4Awq1C7DmJdoP/Q5cZh2XCrUM13zow95F7OCvw15rhdoI+p3r5kIPHycZvJfYTYIsGdtjOOt9ATe3v4f+8L0VYug/EhB4AR/AzsYXNoG/gd72VXa8RMM1KSIljXCmvYPBwT34ZPNjI0iSHAutmI4cOwPiWSgz4a7Z4qxolMW5tvkETkYoAN7DsPcl3FjJEgTl668VzoTZ7+G0+xDWllYXQqhhXvjozl34BEWY6BeLZ+UeHJ5EAns8fAmP1q9lip0EHRW+zNSn4xM4vHUbtu7gdRfdeKZMG/0Ljr57BUMM1fEQ/vn1XVgTOUmdWWnHTHH6lhTirpi7/Ppzvks4gwq1ZMAikNtsdOEC1KkDzuFp/odUqOFtWw2FGgksP0G9gR+/ewGn5iaaxXkiOb2DwfMXMDBlUNjtlhMj84++3BalpJF7wiQHMSlurKZu9JJV4cjmQ/h8+w6sNVyoRTcHXswZjqbv5Ofiz6TjSnwbw6j/DWx99hlsrSyGUItA2Ws/cd1buGJMR+ULb0hKMMaLzMOnYkwaI97Brz++srnQWmVm0rz45QZPuD0PnL5p2bhtSdHPfi3Vvks4Awm127CzjdNDzDkWwPLKPdj57Fp6pMQb2l9eugJbna4ZoQDAC3cfbpjROFbn6Bj21ldheYmmkYSpTy56en02fbABO90TGAEfjl6FG3ZUxFDppnIfwNEwnqR1I4M0vTpNG77PXJtsyuxiB/qmeRxe78Hh9oYVvGjvAfTYsLKz7eJj6P3yAvb84ecEzxuw891xdOeDdri278Fh7+/xuUteOWOzHSUy/KOtG7Bz0IOBuePHArEvLn/1FF7sWps3DiKxkrADz+f+fg1Hm5cSot6NLjobC3wCVMd1eNx9Co9snETTKMU8+m6JINPUfbLtZFkSc+kR5UQ5wiEl9UTBen2RkkZwCwuTne3IO6/g1Ajeho+omY6OcpxlG/dlTrGV98hc/FnenKgk5vXNb6B/+hJ2miLUwOaF9X3ouxyJ+24t1oia9WWhYGE+N2UTuNnBKTbPI3YLcRfmruqAJZyBhNoDeNb71qzZoVGzCCB2Xl34wZ/SclMYTJzQWox7XavOaW3QBVg2nT0buXBBEIsDt0bNiah03Sguojvy5DF3h0Od6VKyY3ZiKCXUkvUgwYVt+H5zbbK6rFCL1uOw/TSNzIbTnW10jH+uP4QdEm5uPxO+UtuuHO8oaFoibUs8PcN84eqw4qXQ3ySyeP12GtjZWOATJ9R4HRHWMjz6bsGbBRoFi+IvXcLsceswhTWa/BS6ceE3M/x4TbelpBHc1KJkRx356IP1ScOFGlDuuwJbBz/DaHwKvT/twv7xcOq1W3PxZ6UAQayfwl7/LYAVqIuxRg1B5oyoscGGKEe+g2GvAztf/xTfKFfiKbvwPHxaKFiMefZmfvO/oDd8n23whEfmgdM3rRB3Ue7yKyzxXcIZTKgdvX4VrbMyooo6Oey8fklNaZGIW3aCiwkBN5qEs2E0gnYVPv/LN3DfrAeI5/z5KI4k1JyIcPXgegI6n5LhBVimNsuKAiYGK7chOcrVx9eo0UiNTdbmvDM4ObiXmEKLhRqV46ORF0Cyj8R0PKK2Cjd2XybXGKDYotEfEiOOO/TNz3BoRCAJPy7UbkWJFz7AaPQuXsOV6++Mqc+yPuFCjdoZ/wdG//m3XR9G/CCRaR7TbolvDJyQTxeKsRVOx5E/w03tCOYE3yUljeCN5CY71pE78dx0ocbW+pibnnB45+LP0gFCI6X2IZtGCTUk4T0Mj/9sHyaY3XU/D58WChbqI0y80uxV6UAoVXAeOH1DCnHn5i6/tnLfJZzhhNpwyBZMv2bbb1JCjcwdD/vwt24Xjg627TQnEwemUFJ04HTZ/e5v7K6SiYPUaBcJCKwoFgG803UiZ2KhNkEbBJ5/SkLN7eMjRGzbiiiHgUQV1uvOle1LC7XkaFV0Z4ttRcLRtcFGyjCY6D/ilPmCpjs5RtP35Pk79pGzD8+vLNS8hOi4iO0lu80n5y1hb4Y9iTKxmMsddTPnlKkvUXktviBHM//LTHZ4/X8Lj9w1TzeA4YQLYZsLTmqs1OcZDLrfwF7nsyg3rn8ZZJSiVjhHx7C/+zxe39Q4oYZLLp7DXucx7JilGBvwqHfK+q9SgVBYaB4+LRQs1srx8BiemKU6fl9dCKOwwDxw+kYU4s7MXX5N5b9LOAMKtfd2WmIVbn71GD7H0S/TYQsdlBuNETpPEk2EyxKBxi+vPISjUz6kysRBSqjx0SnBBqNn7FOp1KYoCgK3Qbj4pxMTzGZni8CREUmRuHIiijBgvVJ9TKw6IURt8HNT57+NX4HCxJnxB3033Mc8cTFsYJbyt+wjWajFbbmRVDeixsUpF3r5PHJ3RNvxdKzjK1WIRskK1qdFJGTesKSqrdEOKWkENy8r2fkdeWtG1HDE91P4oxWo0dOCqxDPQEzugbn4s5R5b6H/9eNkPm+UUBvD6OQJ3P+DXcqD09dm3S7NNpQiqVShefi0ULBwS7OuZ15mgu154PTNKsQ9A6wSzoBC7QMb/cBOkUY2/A6YjUKsb8Nh9x/mAQJRcACbErWiYM2tYUNKhQ67rEipu1BzQ8lMvPlRJGEwtEiv+/D9wEWMN0KRaPssXqvlC7qEPbEvksKmrL8F+7B+EpOJdYNxW2mh5vGVwFLlLWYZ9nDMrm5PHPIybrtEfa5sfTakpBHcOjHZ0ehZlsCmG8Ew1swFZ0lTo87BuybN8o1LU7+6ojY43bWT5V8Pf0nueLHZY7W5TRqVNzHt+8sut8mYceC2V9mePU6wSzzK5Dm0POIldcNeBZRQdh44/WabKdRswkVC4ydA/Q6KjUKQ6HJ3G2y9GC7GPHli5/evwNZXX7rtePpT6LCnEWouecTDtu5uFjGFGLXzIwG/izYznuh9SownughEgSvW5/uBiyB8mrQbPcFJ78FBvJSAGC9mcbOZxsR3AuETuHTxxr5ICjWGI9ffgn3IDWub/C76xI2oeUKNnr5aYuv1BB7TbokFJnHtl4kuYox1b+rYL2i+Ew90AyMWqt3OuSRHUahJVJB4m74T92ufC06/UfF7FkaMn2vNEWoSdnOth7s+Zu/THKEmYrG+bbxQw1jd8JYpSQ6vtm/2/kzb00yhRk/B8E4+NeWWHiVDByxfuw43+MsD3QMA9PQhP4+Gj2NxEEREiU8nrsLv169FbwiflVBLCFwSq1yoenedbFF/GKHm1Y/+SKwHjBffG1+Z49E57mEFNrqZFGrcb6wd3988dkz9VnCV9UmmUCvHo3CJxiOJUmLldpGgTVcS73E+JmEbH6rz1lySowq1ZAjY3BdfWzaGL/pLP5Knlfk2F3+WMUQqI4obqWC5fbPHmiPU6MldlqujB7CuL6SAyRQsJg9eZa+5il7OfJMGF8q5qlSp2fszbUYmbipaOnfRCcWfEs6wU5840mJ/WicehRBGSsZD6H9HDxDQu8x+te/Swo7sf+3P9lxIrsvgnaN5su99vH4qkIiKF0OiqIjeFfZL73H0CwuB2ki7ij8dxDH77//CUaHkT8mEEWoP4Fn/J7sIFEfSpJ868d+jhu9BeyG/R83/qbBCf78xlCR+hmSJxDi+7JoWqOb4JFOoYdXFPKZ9wkbzEkKM3RwwwUoPXoj14E4aGUzUlVm6NgekpBHOOBo9YgI+9+lZKt/kEbWI3WTMp6/7SX0wW39OapU9b5GEGl3PLgcII4GJvJeVV6fkbOa/aUozAewaTdy4ejfx2Hd0+8FfQYIszTd2i3BTLmK85Oau8n6WcE4n1Mq3rSXryIC4/quOhp6XTXSxTjsKFl/U8Q3MeWGq1q6UNKrVsBilFedi+KmKlerTKmzVv2yb/alCrf7xOTsLVagVcBu/HmY6gUWCL/xIUAGAqQ+3OTlOTV4NK2iLP5H6tmBVnDW80KYwSfKnCrUpCF34U1WolXChFVlTTFnSLyNMJ/ZKmDqDIlLSmEEz516l4jx3FwQ3QH0anNJzrbDN/lShdq6hp40rA/VmoM3Jsd6emcy6tvgT2WkLVsU52bVQ17Mkf6pQq6u31C5loAYMSEmjBmYFN0FxBqf03CtUn567C4Ia0GZ/qlALGkpamTLQLAbanByb5ckITVv8iWjbglVxNutKlfypQq1ZPlY0ykBQBqSkEbSBmlSmOGviiIBmqE8DklmDqtrsTxVqNQhANUEZqCsDbU6OdfXJNHa1xZ/IUVuwKs5proj6nSv5U4Va/fykFikDtWFAShq1MS6gIYozIJk1qUp9WhNHBDKjzf5UoRYoiLQaZaCJDLQ5Oao/F5sBjd3F9p9vfZv9qULNjwb9rgwoA46BNidHR0KDNtriT3RZW7AqzgZdoBlxmxJq6HT9Vw40BjQGNAY0BjQGNAY0Bs4nBrj8TAk1flC3lQFloN0MYJJuw5/ibJ6X1afN8mmb/alCrVmxrGiUgaAMtDk5BiWyJpW1xZ9Id1uwKs6aXFyBzJD8qUItELlajTLQRAakpKE4F5eBtvgTPdQWrIpzca9HyXLJnyrUJKZ0nzKgDBgGpKTRRGoUZ/O8qj5tlk/b7E8Vas2KZUWjDARloM3JMSiRNamsLf5EutuCVXHW5OIKZIbkTxVqgcjVapSBJjIgJQ3FubgMtMWf6KG2YFWci3s9SpZL/lShJjGl+5QBZcAwICWNJlKjOJvnVfVps3zaZn+qUGtWLCsaZSAoA21OjkGJrEllbfEn0t0WrIqzJhdXIDMkf6pQC0SuVqMMNJEBKWkozsVloC3+RA+1BaviXNzrUbJc8qcKNYkp3acMKAOGASlpNJEaxdk8r6pPm+XTNvtThVqzYlnRKANBGWhzcgxKZE0qa4s/ke62YFWcNbm4Apkh+XM6oTbswpb5bdBVuNE5hlHC0NdwtHnJXCyXO334kDg2wy8f+rB3EX+b6xJsdV/PsKEpqx4N4IfOXVij31bdOIDB2K/zAwy7DwyHy5tdGPqHJ/o+htHgR3jW2Yb9ftJj1aubhX3Vrcg9w8XoAzgaVonCkDzlWugdfAv9zi1YXroNh4N39tgI+p3rURxQvJhPxDSCwcFt4dh12OuPYDw4gJtL0vXpNZvxVUoaGUWr7z7rwc6K9Dt6q3Dz4ATochgPj+HJ9kaEceUu7L0ceLmmetP+GeFwnsGg9xyede7C5e0enPkNed/Hp124v8J9bQuMh/DPryk/bMBO9yQI5rniHA+h/9023DCxegW2Oi9gMCKvEhHRdXb0tANbF3ehd+Yfp3LVP8NhzWg7Fb++H89g8HIftijGax+7Es7qGDJjWqq+wr5g/hwNoNf9K+xtbsBO741sAY/dlbuwfzx0+Sg+YQxnvd24D8c4F/vx+IwyWxLOQEINk+0t2Ou/ZXaoUGNkeJuCgy92oJ/SETMQQk7IRh25Z1jFrzOwr6IFhcUnFWpBeSq00hWIhNUFWEt18jxmrsDWwc+JjpvOW0ZRtvsShq6/ewO97aue8HPNFW5ISaPwpFIFOB5frLEOb3QMexv3bKIcw+jkCWytXIH73d+ExFmqYbFQGJzvYHBwDz7Z/Ngk77QPvabHv8HRvSuCb97C/3Sfwj+H7wHgPQyP/wxbK1ezOxWv2ryv88OJNxx3YOvrn6JYHP0Mh5tXYO1eF05dbIK5kfjozl34BMXMyiIJtfdw2n2Y00nb4yv34PAkkuvj4Ut4tH4tiB+5j8P4lNdI2xNgyIxpqnPyzyA4xydweOs2bN3B6y7rmsLY/djl0chvH3v6BgAcVspfyRvMSZFKOAMKNV9NqlDLdhQTOLkKnJULNaIWVIDMwL5s0iY7slBCjUSVlECYsEl1aOWOFQoHgWEpaQjFJtj1BnqdfegZMcJOx1GKWzS6jMLntidaqfOocaeOncHGqmc3w2g2sTN4CJ9v34G1xOgpwPjXn+DHUxRp9BfFxST+oxroM6g/c3CaGwcvTqORFim2Iz8vlFAzNxBfZI8AitxI8UyemfwzqE+5GZUxZMc0r3bS7ZA4oxtbKRajm4ebidi1+TXRV49h1N+Hm6kb6knRxedJOMMKtSV+pysItYxO80O/A5dx2JDECBcTvT6bIqQpAD4cuwo3tr+HPiV8d+4l2Hr6ik0fSEPvOE1xADvrq3bqaAN2DnpseD4WIpe/egovdu30S8JhMcHRFtb537C3iYodlTbadwC9AU2CxLxEx7FM1jRt3D5yc8qngNa34UnfG47FIV2cQqCh9iUPj+Of7gAuwLI4kkeY3sOw32VYLsDa5j784LBUtA+KuCnbri1XhBeLOcx86hOnW14kcC3jtES3H939u3MknopiBgDQrgOa8pFigHB6n24qhdtKZUjESaNt8TFx6J3wJJIP1Zv/KSWN/DNKHh3/Gwa/0jVB52BHdiee9jQdxaX4uy2Wl2SppqqfQXGKHRy3CJP8N7DVeQWnZuqEjSDyYrRt6hPu6Ol4hc/54LTCy8+TmbwsmlCjGyPM7X+Bo540FW+vyfV96LvpXtx3a4FG1KpgqBjTFWKWioaM3ewckhG7Jjfz65RyLvaxXda/k7WTf0o4Awm1K264f3nlIRyZu8FYkLg1atRhLCU7omyhxjpKI3rw+4a9C00ec3ebTqgljyN4/F/bfAIn5sIRhq5TZZgQce1LHSU55QxODu4lh8PdeTQ1HPNCNpUSaut3YMsJSsLGAsdOLcR1UpkLsEzJwvHPjmUKteiOIVpfwsojHudjxk+RfVCGG+SxTLsohqKplFy8WJ3DHMdcdGfvYTJ+sjca7hxWxvBUJmbwrhLXmLFzaZv8QOGS+KTk749M20K2k0Phz9dvmaMu5oVjWMCdK99BJszwviCOuf2hnbc+tfkDAExyFDBl7Z/C0KA4MwWJNRBHYza/gf7og13jwq7jBAa8oejB4fYDeNQ7DTLVOx+cthPzhRpk7V8woeauJ7rGUbB12Q0+OjHOY1Gf8w6GvQ7s0FRwws/TfQnq04QpFTCUjulEA5W+hMSZKdSyrl0v50Tnk//xkwaRKkESC0s4Awm167DXewl7VkhE6xBiQTKNUHPCCgOBhIqb92edIgkO12mhQPnSTq28h2HvS7uo1XZWhngUHfEagrjzpw6NCRG3Bu8DjEa0yDvJc+w8toZofAo9GolzHTWrl0YRk1XZb6wcC4RozhxHAWkkziY6I6JiPHE5tpjc8VOwRs0lI7bmiWGJhHFZ++xwshVDbn0Vq8+JyVLtVsDrRBcJNTqXccLWGrhYlXgqEzPuPIohFJUUu4LocH4nu+QbgTi2eHLwt7M6fLr7y2vfGZLYkJJGokDAL4jxIz6VQLHgd/jGD4zfADYExZmV7I2dmLM+tetdSJxLfiOfoY8lITAZ6PngpFj2cUWY3E21g2DLTzDi66oQNoJiFeoHXHD+/C92RoblE1eW1hdGPkzdYLly023MFmcZDGVjuj44o3wq5BBPkDmLM/aPh334m5s9ocEYd9ZEG5I/wwm1/pmZs41GYNDgf6Wf+kx1mhGO7BE1TmT85Bu/0N25KaFGIoa4ihMfdsbvaLqVRju8z5QQ8TsLqtZ9UnISRkSog18iccQETlmhlmifsFiM1KGlRluoI2BTnE5IkC0OQHIjw1fJQgxHnn1QgZsy7VbBm1kfTuv+A466T+GQnijEEVcSCgJPLta8WMELC//NuUz0LS/hdPtf4ajbhb/509RJIlHNuSc7nVh0ZRh/qc6M+SB1jCrIq5vKyJ9S0pBLTrsXMT7wpoUofvmNDz1J6IuA6doPijNTqOEIxbfwyD0IQfhysLCnz/yF+JMgng9OGg1NzmAM+9/Dznp6KhsoP2TG7yRI5/h6DrrhTNmPI6LPYa/z2Iq5jWAjo5yRoD7lFZvtIgwTxHSqjXI7QuIMJdTIchoUcf0HHZjgU8IZUKjhqx7YCBebCnMdj9hpso6GRIvQSWZ1ZK7zTAk1X4jwzuoVvKbXXmR0utF6udi2Ygfw+r3XkTg8JB7jet26PNGhWeWoLVufq9/HDOD4oenmnLLchNR5/KDbLmlfnghx9kRYSrXrzimBNxVz9OSgPxoVfXexmmqDYc2NGYDE6yR42fVdOHLr+xyJdkMYgXZFSJgzIVnqGBWieLkADh8dKviUkkbBKZMdRnFzS1qczdejovD9PhLWiRuDyZrkZwXFmSXURsewv/ucPfVYQqgZI61QTwkBjqDc9lxwGlOS60DXNjvwzIw8SKI0HD7OQlCsvGJpOzXKG+WZ+3+wT7mSmHMzM1Ilk+2bHc4SGCaO6epYQ+LMFGpZ127GiFqMwl7LM7pGAwu1+E4KSaV/1zmkOk2EyTrAoELNn+aJO7vLnWP4P3r/CQm8mHG2FdvmMLCjyU026uF3IiFG1Igb0yh1vPMYUZMSKyGP+UkKTs8+umPGmCjixsVITrv2Ykqv16KOj40guvrs1Cc71ywEfo4PEJC9TMikhJpQN9GQ+YkPHjyHI/POHvtwiY/fnSvYQMdc/PARZnvQHaObADqJf+bUzYsJ2yGTo1C925Wa9nRHvA3jv5q/4kBM9ix+WG6kHGk+M2NDehLN46Xk16D+FHFmGRLlR/mGtwFCzXBxJ373ofnujx7agYwcP2exl7c/qE95Q4UYpotp3lSZ7ZA4M4Wa7av8OI3K5/RJuCoR31kZwLcSzvBCDdILrp3IcZ1K/HQoDRmica6zT3WS6Ea5s3EjMCS43Lm4Ro1GMHLWqOH0lH0nVWwLdYixEHEYciIqciYK1LhOcHdSbFG/JE7FeuP2HTemHHFBnTMTiWzNXYyHrZ9w/KRHoxIm2CRs1se493KxBwJMQJa1b8o1avxBBNNuBby+UCuIQedniSd2blbMxA8q8GkOdk1kXsgxJj9JuBgX7tbimMtLInST4t+8JDwufpGShlhwqp2I3Z/2FCo019It4eXaQtmKu4LitNeO78e0SdTR5fkOz4rKXfbeQZaur3jP+eC0+det0fXttLEvxLdfssr3oFiLGj7rwaNd9oJjkyv86836OzMHFDUiH58ZzokwlI1pGUve3pA4o7xJ/XyyVXMsEYtl/IZlHsOjrBfoJpvI/SbhnIFQw7xCL3L0ppO8/WgQCoHfr1+LnpSkUSOpk5xEqAl3rvE6DyY6vHLuAQYmqFwHnksxm/r16ky+EDhL4PiVZ5XzhRpfsB6PZEb8coGIvone8eSOkcD1m2ZPLbmyDhOJkAr28WlxVw/Zyhdhxk8aZbdbAa8v1Api0HWuIk9lYiYvBuIblBTdtjM2v1TBEzl/ujWRPNCX7EEV9yRuuubY53JiEs5wu9AHM/9DrsVpT2qZXutyPX6BKh0K9BkU51RCzYp69vodc8O18cC9OHUayPPFidOf+Csod+Hy5p/tC3wl6xdLqJkF5GYkPsIyHv4E+9sd752ANg+wG+foYbXrNX1Zs+SXSTAsvlCLlnDlvfA2Wt8crzvGBy6+hZ0/8ReNS3yW2yddo7MRaqYPwZ9G8YQa7ufvArPv+fql9zj7PWruZ45InLDpKZw4pYcCSHA4kRe9Ry3/J0z8d2L571qLhUg5oYaOoE4l6z1qWCauNzlS5jsyqxxxQSNq9rwy7xVzbzq3IinzLhfrlN6j1oEjtzC+on2luCnTbgW8vlCTYvC7Yxie2p9Dc2KIP+3ExW5RzKBtfhk8fxsOxfctWSzmNPuTSsYGenUDiVn6xJHQs/RPlxjxmzFKSiOBDhtrs2BTShoFp1Q+PB48gfupn6DDauKRwOS7CCs3UXhCGJzUSZGv8DNvtIzK8zL+GkrMSd34PZGFSPILzAcn4SoR9xSb7ubNH4XKx5N3NAzWdAvxTLdgK6IAAAJBSURBVAW+NeAu7D390Xs1hz2HPQiCtpiytf75szRW82Sr+xmwMhjI9zymhXon2BXGn5RT2DXKb4zJLv4TbuymKTrMZ+jwgZkOPCvK7VRviU8J53RCrUSjWkQZUAbKMkBJpPrIV3YLlDilBxGyz6IjUtKgY036VJxN8maERX3aLJ+22Z8q1JoVy4pmoRmIp33dFOzUeEj8TXaH2+bkODX1NaygLf5E6tuCVXHW8EKbwiTJnyrUpiBUT1UGwjNghdUE05SSLfRww6TCT0oaUjuLvk9xLroH0/arT9OcLPKeNvtThdoiR67argzMmIE2J8cZU3su1bfFn0huW7AqznO5lGbWqORPFWozo1srVgYWnwEpaSw+qjQCxZnmZNH3qE8X3YNJ+9vsTxVqyVjQb8qAMsAYaHNyZDQ0ZrMt/kSHtQWr4mzM5WmASP5UodYsHysaZSAoA1LSCNpATSpTnDVxREAz1KcByaxBVW32pwq1GgSgmqAM1JWBNifHuvpkGrva4k/kqC1YFec0V0T9zpX8qUKtfn5Si5SB2jAgJY3aGBfQEMUZkMyaVKU+rYkjApnRZn+qUAsURFqNMtBEBtqcHNWfi82Axu5i+8+3vs3+TAk1JEP/lQONAY0BjQGNAY0BjQGNgfOJAS5UE0KNH9BtZUAZUAaUAWVAGVAGlIHzZUCF2vnyr60rA8qAMqAMKAPKgDKQyYAKtUxq9IAyoAwoA8qAMqAMKAPny4AKtfPlX1tXBpQBZUAZUAaUAWUgk4H/B65ag3kSr4ZQAAAAAElFTkSuQmCC"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> can be modelled by the regression line with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>a</mi><mi>T</mi><mo>+</mo><mi>b</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the regression equation, estimate the number of hot chocolates that Lucy will sell on a day when the maximum temperature is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>°</mo><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>eg correct value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> (or for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>962839</mn></math> seen in (ii))</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>84636</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>221</mn><mo>.</mo><mn>592</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>85</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>222</mn></math> <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>981244</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>981</mn></math> <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into their equation <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>.</mo><mn>85</mn><mo>×</mo><mn>12</mn><mo>+</mo><mn>222</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn><mo>.</mo><mn>435</mn></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn><mo>.</mo><mn>8</mn></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>sf</mtext></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn></math> (hot chocolates) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> be two independent events such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>'</mo><mo> </mo><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>16</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>′</mo><mo>∩</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>36</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo><mo>=</mo><mi>x</mi></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mo>'</mo></menclose></mrow></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><strong>EITHER</strong></p>
<p>one of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>=</mo><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>16</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>=</mo><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>36</mn></math> <em><strong>A1</strong></em></p>
<p style="text-align:left;"><br><strong>OR</strong></p>
<p style="padding-left:90px;"><img 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"> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>attempt to equate their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo></math> with their expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced></math> <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo><mo>=</mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>⇒</mo><mi>x</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>16</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>36</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>24</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempt to form at least one equation in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>B</mi></mfenced></math> using independence <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>∩</mo><mi>B</mi><mo>'</mo></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>×</mo><mi>P</mi><mfenced><mrow><mi>B</mi><mo>'</mo></mrow></mfenced><mo>⇒</mo></mrow></mfenced><mo> </mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>×</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>16</mn></math> OR</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo><mo>∩</mo><mi>B</mi></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo></mrow></mfenced><mo>×</mo><mi>P</mi><mfenced><mi>B</mi></mfenced><mo>⇒</mo></mrow></mfenced><mo> </mo><mfenced><mrow><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>36</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo><mo>=</mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>24</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognising <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mo>'</mo></menclose></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>16</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>24</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>36</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>24</mn><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mo>'</mo></menclose></mrow></mfenced><mo>=</mo><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo><mo>∩</mo><mi>B</mi><mo>'</mo></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>B</mi><mo>'</mo></mrow></mfenced></mrow></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>24</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>4</mn></mrow></mfrac></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> minutes, taken to complete a jigsaw puzzle can be modelled by a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>6</mn></math>.</p>
<p>It is found that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>%</mo></math> of times taken to complete the jigsaw puzzle are longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo>.</mo><mn>8</mn></math> minutes.</p>
</div>
<div class="specification">
<p>Use <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>32</mn><mo>.</mo><mn>29</mn></math> in the remainder of the question.</p>
</div>
<div class="specification">
<p>Six randomly chosen people complete the jigsaw puzzle.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By stating and solving an appropriate equation, show, correct to two decimal places, that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>32</mn><mo>.</mo><mn>29</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>86</mn></math>th percentile time to complete the jigsaw puzzle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly chosen person will take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to complete the jigsaw puzzle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least five of them will take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to complete the jigsaw puzzle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Having spent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math> minutes attempting the jigsaw puzzle, a randomly chosen person had not yet completed the puzzle.</p>
<p>Find the probability that this person will take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to complete the jigsaw puzzle.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>~</mo><mi mathvariant="normal">N</mi><mfenced><mrow><mi>μ</mi><mo>,</mo><mo> </mo><mn>8</mn><mo>.</mo><msup><mn>6</mn><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>≤</mo><mn>36</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn></math> <strong>(A1)</strong></p>
<p>states a correct equation, for example, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>36</mn><mo>.</mo><mn>8</mn><mo>-</mo><mi>μ</mi></mrow><mrow><mn>8</mn><mo>.</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>5244</mn><mo>…</mo></math> <strong>A1</strong></p>
<p>attempts to solve their equation <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>36</mn><mo>.</mo><mn>8</mn><mo>-</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5244</mn><mo>…</mo></mrow></mfenced><mfenced><mrow><mn>8</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>32</mn><mo>.</mo><mn>2902</mn><mo>…</mo></mrow></mfenced></math> <strong>A1</strong></p>
<p>the solution to the equation is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>32</mn><mo>.</mo><mn>29</mn></math>, correct to two decimal places <strong>AG</strong></p>
<p> </p>
<p><strong>[4</strong><strong> marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mrow><mn>0</mn><mo>.</mo><mn>86</mn></mrow></msub></math> be the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>86</mn></math>th percentile</p>
<p>attempts to use the inverse normal feature of a GDC to find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mrow><mn>0</mn><mo>.</mo><mn>86</mn></mrow></msub></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mrow><mn>0</mn><mo>.</mo><mn>86</mn></mrow></msub><mo>=</mo><mn>41</mn><mo>.</mo><mn>6</mn></math> (mins) <strong>A1</strong></p>
<p> </p>
<p><strong>[2</strong><strong> marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of identifying the correct area under the normal curve <strong>(M1)</strong></p>
<p><strong>Note:</strong> Award <strong>M1</strong> for a clearly labelled sketch.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>></mo><mn>30</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>605</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2</strong><strong> marks]</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> represent the number of people out of the six who take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to complete the jigsaw puzzle</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mi mathvariant="normal">B</mi><mfenced><mrow><mn>6</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>6049</mn><mo>…</mo></mrow></mfenced></math> <strong>(M1)</strong></p>
<p>for example, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mrow><mi>X</mi><mo>=</mo><mn>5</mn></mrow></mfenced><mo>+</mo><mi mathvariant="normal">P</mi><mfenced><mrow><mi>X</mi><mo>=</mo><mn>6</mn></mrow></mfenced></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mi mathvariant="normal">P</mi><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>4</mn></mrow></mfenced></math> <strong>(A1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>241</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[3</strong><strong> marks]</strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizes that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>></mo><mn>30</mn><mo> </mo><menclose notation="left"><mi>T</mi><mo>≥</mo><mn>25</mn></menclose></mrow></mfenced></math> is required <strong>(M1)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1</strong> for recognizing conditional probability.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>></mo><mn>30</mn><mo>∩</mo><mi>T</mi><mo>≥</mo><mn>25</mn></mrow></mfenced></mrow><mrow><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>≥</mo><mn>25</mn></mrow></mfenced></mrow></mfrac></math> <strong>(A1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>></mo><mn>30</mn></mrow></mfenced></mrow><mrow><mi mathvariant="normal">P</mi><mfenced><mrow><mi>T</mi><mo>≥</mo><mn>25</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>6049</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>8016</mn><mo>…</mo></mrow></mfrac></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>755</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[4</strong><strong> marks]</strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All answers in this question should be given to four significant figures.</strong></p>
<p><br>In a local weekly lottery, tickets cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2</mn></math> each.</p>
<p>In the first week of the lottery, a player will receive <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>D</mi></math> for each ticket, with the probability distribution shown in the following table. For example, the probability of a player receiving <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>10</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>03</mn></math>. The grand prize in the first week of the lottery is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1000</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>If nobody wins the grand prize in the first week, the probabilities will remain the same, but the value of the grand prize will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2000</mn></math> in the second week, and the value of the grand prize will continue to double each week until it is won. All other prize amounts will remain the same.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether this lottery is a fair game in the first week. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the grand prize is not won and the grand prize continues to double, write an expression in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> for the value of the grand prize in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mtext>th</mtext></math> week of the lottery.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mtext>th</mtext></math> week is the first week in which the player is expected to make a profit. Ryan knows that if he buys a lottery ticket in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mtext>th</mtext></math> week, his expected profit is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>p</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>considering that sum of probabilities is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>85</mn><mo>+</mo><mi>c</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>03</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>002</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0001</mn><mo>=</mo><mn>1</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>1179</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced><mo>=</mo><mfenced><mrow><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>1179</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>10</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>03</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>50</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>002</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>1000</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0001</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>7358</mn></math> <em><strong>A1</strong></em></p>
<p>No, not a fair game <em><strong>A1</strong></em></p>
<p>for a fair game, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced></math> would be <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2</mn></math> OR players expected winnings are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>264</mn></math> <em><strong>R1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of GP with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>2</mn></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo>×</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced><mo>></mo><mn>2</mn></math> <em><strong> (M1)</strong></em></p>
<p>correct expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>w</mi><mtext>th</mtext></msup></math> week (or <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mtext>th</mtext></msup></math> week) <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>1179</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>10</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>03</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>50</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>002</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>1000</mn><mo>×</mo><msup><mn>2</mn><mrow><mi>w</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>0001</mn></mrow></mfenced></math></p>
<p>correct inequality (accept equation) <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>6358</mn><mo>+</mo><mfenced><mrow><mn>1000</mn><mo>×</mo><msup><mn>2</mn><mrow><mi>w</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>0001</mn></mrow></mfenced><mo>></mo><mn>2</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>></mo><mn>13</mn><mo>.</mo><mn>642</mn></math></p>
<p> </p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>-</mo><mn>1</mn><mo>></mo><mn>3</mn><mo>.</mo><mn>76998</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>76998</mn><mo>…</mo></math> <em><strong> (A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced><mo>=</mo><mn>1</mn><mo>.</mo><mn>4358</mn></math> in week <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced><mo>=</mo><mn>2</mn><mo>.</mo><mn>2358</mn></math> in week <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> <em><strong> (A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mn>5</mn></math> <em><strong> A1</strong></em></p>
<p>expected profit per ticket <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mtext>their E</mtext><mfenced><mi>D</mi></mfenced><mo>-</mo><mn>2</mn></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>2358</mn></math> <em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>
<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <em>χ</em><sup>2</sup> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the associated <em>p</em>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether you would reject the null hypothesis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that this flight arrived on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>The arrival status is dependent on the distance travelled by the incoming flight <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “associated” or “not independent”.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60 \times 45}}{{180}}">
<mfrac>
<mrow>
<mn>60</mn>
<mo>×</mo>
<mn>45</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60}}{{180}} \times \frac{{45}}{{180}} \times 180">
<mfrac>
<mrow>
<mn>60</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>180</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into expected value formula.</p>
<p>= 15 <em><strong> (A1) (G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4 <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if “2 + 2 = 4” is seen.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9.55 (9.54671…) <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(G1)</strong></em> for an answer of 9.54.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.0488 (0.0487961…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Reject the Null Hypothesis <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their hypothesis in part (a).</p>
<p>9.55 (9.54671…) > 7.779 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>OR </strong></p>
<p>0.0488 (0.0487961…) < 0.1 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(R0)</strong></em><strong>(ft)</strong>. Follow through from part (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for a correct comparison, <em><strong>(A1)</strong></em><strong>(ft)</strong> for a consistent conclusion with the answers to parts (a) and (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for <em>χ</em><sup>2</sup><em><sub>calc</sub></em> > <em>χ</em><sup>2</sup><em><sub>crit </sub></em>, provided the calculated value is explicitly seen in part (d)(i).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{52}}{{180}}\,\,\left( {0.289,\,\,\frac{{13}}{{45}},\,\,28.9\,{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>52</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.289</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>45</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>28.9</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{35}}{{97}}\,\,\left( {0.361,\,\,36.1\,{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>35</mn>
</mrow>
<mrow>
<mn>97</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.361</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>36.1</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{14}}{{45}} \times \frac{{13}}{{44}}">
<mfrac>
<mrow>
<mn>14</mn>
</mrow>
<mrow>
<mn>45</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>44</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correct fractions and <em><strong>(M1)</strong></em> for multiplying their two fractions.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{182}}{{1980}}\,\,\left( {0.0919,\,\,\frac{{91}}{{990}},\,0.091919 \ldots ,\,9.19\,{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>182</mn>
</mrow>
<mrow>
<mn>1980</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.0919</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>990</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mn>0.091919</mn>
<mo>…</mo>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mn>9.19</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1) (G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The flight times, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> minutes, between two cities can be modelled by a normal distribution with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn></math> minutes and a standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> minutes.</p>
</div>
<div class="specification">
<p>On a particular day, there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn></math> flights scheduled between these two cities.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> of the flight times are longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>82</mn></math> minutes, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected flight will have a flight time of more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that a flight between the two cities takes longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes, find the probability that it takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>82</mn></math> minutes.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of flights that will have a flight time of more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> of the flights on this particular day will have a flight time of more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of inverse normal to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-score <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>0537</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>0537</mn><mo>…</mo><mo>=</mo><mfrac><mrow><mn>82</mn><mo>-</mo><mn>75</mn></mrow><mi>σ</mi></mfrac></math> <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>408401</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>41</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of identifying the correct area under the normal curve <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>80</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>071193</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>80</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0712</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>80</mn><mo><</mo><mi>T</mi><mo><</mo><mn>82</mn></mrow></mfenced></math> is required <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>82</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>T</mi><mo>></mo><mn>80</mn></menclose></mrow></mfenced><mo>=</mo><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mn>80</mn><mo><</mo><mi>T</mi><mo><</mo><mn>82</mn></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>80</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfenced><mfrac><mrow><mn>0</mn><mo>.</mo><mn>051193</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>071193</mn><mo>…</mo></mrow></mfrac></mfenced></math> <em><strong> (M1)(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>719075</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>719</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of binomial probability <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>64</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>071193</mn><mo>…</mo></mrow></mfenced></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced><mo>=</mo><mn>64</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>071193</mn><mo>…</mo></math> <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced><mo>=</mo><mn>4</mn><mo>.</mo><mn>556353</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced><mo>=</mo><mn>4</mn><mo>.</mo><mn>56</mn></math> (flights) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>6</mn></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>7</mn></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>6</mn></mrow></mfenced></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>83088</mn><mo>…</mo></math> <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>1691196</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>169</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the data collected from an experiment.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The data is also represented on the following scatter diagram.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> can be modelled by the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this model to predict the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>18</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>x</mi><mo>¯</mo></mover></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>y</mi><mo>¯</mo></mover></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line of best fit on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>433156</mn><mo>…</mo><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>50265</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>433</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>50</mn></math> <em><strong>A1A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>18</mn></math> into their equation <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>433</mn><mo>×</mo><mn>18</mn><mo>+</mo><mn>4</mn><mo>.</mo><mn>50</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>12</mn><mo>.</mo><mn>2994</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>12</mn><mo>.</mo><mn>3</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>x</mi><mo>¯</mo></mover><mo>=</mo><mn>15</mn><mo>,</mo><mo> </mo><mo> </mo><mover><mi>y</mi><mo>¯</mo></mover><mo>=</mo><mn>11</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="padding-left:60px;"><img 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"> <em><strong>A1A</strong></em><em><strong>1</strong></em></p>
<p><strong>Note:</strong> Award marks as follows:</p>
<p style="padding-left:60px;"><strong>A1</strong> for a straight line going through <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>15</mn><mo>,</mo><mo> </mo><mn>11</mn></mrow></mfenced></math></p>
<p style="padding-left:60px;"><strong>A1</strong> for intercepting the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis between their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>±</mo><mn>1</mn><mo>.</mo><mn>5</mn></math> (when their line is extended), which includes all the data for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>3</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>25</mn><mo>.</mo><mn>3</mn></math>.</p>
<p>If the candidate does not use a ruler, award <em><strong>A0A1</strong></em> where appropriate.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>At a café, the waiting time between ordering and receiving a cup of coffee is dependent upon the number of customers who have already ordered their coffee and are waiting to receive it.</p>
<p>Sarah, a regular customer, visited the café on five consecutive days. The following table shows the number of customers, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, ahead of Sarah who have already ordered and are waiting to receive their coffee and Sarah’s waiting time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> minutes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> can be modelled by the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of Pearson’s product-moment correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret, in context, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> found in part (a)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On another day, Sarah visits the café to order a coffee. Seven customers have already ordered their coffee and are waiting to receive it.</p>
<p>Use the result from part (a)(i) to estimate Sarah’s waiting time to receive her coffee.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>805084</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>88135</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>805</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>88</mn></math> <em><strong>A1A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>97777</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>978</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> represents the (average) increase in waiting time (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>805</mn></math> mins) per additional customer (waiting to receive their coffee) <em><strong>R1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>7</mn></math> into their equation <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>51693</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>52</mn></math> (mins) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The number of hours spent exercising each week by a group of students is shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The median is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn></math> hours.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the standard deviation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>recognising that half the total frequency is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> (may be seen in an ordered list or indicated on the frequency table) <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>4</mn><mo>=</mo><mn>3</mn><mo>+</mo><mi>x</mi></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo><mi>f</mi><mo>=</mo><mn>20</mn></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>7</mn></math> <em><strong>A1 </strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>58429</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>58</mn></math> <em><strong>A2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>5</mn><mo>×</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mn>4</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>×</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mn>4</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>×</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mn>4</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>×</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mn>4</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>7</mn><mo>×</mo><msup><mfenced><mrow><mn>6</mn><mo>-</mo><mn>4</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></mrow><mn>20</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>2</mn><mo>.</mo><mn>51</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>5</mn><mo>×</mo><msup><mn>2</mn><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>×</mo><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>×</mo><msup><mn>4</mn><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>×</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>7</mn><mo>×</mo><msup><mn>6</mn><mn>2</mn></msup></mrow><mn>20</mn></mfrac><mo>-</mo><mn>4</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>2</mn><mo>.</mo><mn>51</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><msqrt><mn>2</mn><mo>.</mo><mn>51</mn></msqrt><mo>=</mo><mn>1</mn><mo>.</mo><mn>58429</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>58</mn></math> <em><strong>A1 </strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates attempted both parts, with varying levels of success, particularly in part (b). </p>
<p>In part (a), the most successful approach seen was from candidates who made an ordered list to visualize the given data set, which enabled them to recognise either the number of sixes required for the median to lie at 4.5, or the total frequency. The most common error was to mistake the median for the mean, which led to a non-integer value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>67</mn></math>.</p>
<p>Part (b) proved to be more challenging, with many candidates either not taking into account the frequency of the exercise time when generating the summary statistics or treating frequency as an additional variable and using two-variable statistics on their GDC. With both, this led to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>41</mn></math> being the most common wrong answer seen. A few candidates gave the sample standard deviation rather than the population standard deviation. A number of candidates attempted to use the standard deviation formula but were usually not successful. This formula is not in the course, although it can be obtained in the HL section of the formula booklet.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>
<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>
<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>
<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>
<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0 </sub>, for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(H<sub>0</sub>:) (choice of) language is independent of gender <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “there is no association between language (choice) and gender”. Accept “language (choice) is not dependent on gender”. Do not accept “not related” or “not correlated” or “not influenced”.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <em><strong>(AG)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>16.4 (16.4181…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\chi _{{\text{calc}}}^2 = 8.69">
<msubsup>
<mi>χ</mi>
<mrow>
<mrow>
<mtext>calc</mtext>
</mrow>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mn>8.69</mn>
</math></span> (8.68507…) <em><strong>(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(we) reject the null hypothesis <strong><em>(A1)</em>(ft)</strong></p>
<p>8.68507… > 5.99 <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c)(ii). Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><strong>OR</strong></p>
<p>(we) reject the null hypothesis <em><strong>(A1)</strong></em></p>
<p>0.0130034 < 0.05 <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}}\,\,\,\left( {\frac{4}{5}{\text{,}}\,\,0.8{\text{,}}\,\,80{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.8</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>80</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong><strong><em>(A1)</em></strong><strong><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for correct numerator, <strong><em>(A1)</em></strong> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}} \times \frac{{87}}{{109}}">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>87</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two fractions. Award <strong><em>(M1)</em></strong> for multiplying their correct fractions.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{45}}{{109}}} \right) + 2\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{42}}{{109}}} \right) + \left( {\frac{{42}}{{110}}} \right)\left( {\frac{{41}}{{109}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>41</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding 4 products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.639\,\,\,\left( {0.638532 \ldots {\text{,}}\,\,\frac{{348}}{{545}}{\text{,}}\,\,63.9{\text{% }}} \right)">
<mn>0.639</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.638532</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>348</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.9</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their answer to part (e)(i).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{{67}}{{110}} \times \frac{{66}}{{109}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>66</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two correct fractions. Award <strong><em>(M1)</em></strong> for subtracting their product of two fractions from 1.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{43}}{{110}} \times \frac{{42}}{{109}} + \frac{{43}}{{110}} \times \frac{{67}}{{109}} + \frac{{67}}{{110}} \times \frac{{43}}{{109}}">
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding three products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.631\,\,\,\left( {0.631192 \ldots {\text{,}}\,\,63.1{\text{% ,}}\,\,\frac{{344}}{{545}}} \right)">
<mn>0.631</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.631192</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.1</mn>
<mrow>
<mtext>% ,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>344</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The manager of a folder factory recorded the number of folders produced by the factory (in thousands) and the production costs (in thousand Euros), for six consecutive months.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.30.09.png" alt="M17/5/MATSD/SP2/ENG/TZ2/03"></p>
</div>
<div class="specification">
<p>Every month the factory sells all the folders produced. Each folder is sold for 2.99 Euros.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis and 2 cm for 10 000 Euros on the vertical axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean number of folders produced, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean production cost, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar C">
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{M}}(\bar x,{\text{ }}\bar C)">
<mrow>
<mtext>M</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on the scatter diagram.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a reason why the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is appropriate to model the relationship between these variables.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the equation of the regression line to estimate the least number of folders that the factory needs to sell in a month to exceed its production cost for that month.</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-08-17_om_06.54.04.png" alt="M17/5/MATSD/SP2/ENG/TZ2/03.a/M"> <strong><em>(A4)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for correct scales and labels. Award <strong><em>(A0) </em></strong>if axes are reversed and follow through for their points.</p>
<p>Award <strong><em>(A3) </em></strong>for all six points correctly plotted, <strong><em>(A2) </em></strong>for four or five points correctly plotted, <strong><em>(A1) </em></strong>for two or three points correctly plotted.</p>
<p>If graph paper has not been used, award at most <strong><em>(A1)(A0)(A0)(A0)</em></strong>. If accuracy cannot be determined award <strong><em>(A0)(A0)(A0)(A0)</em></strong>.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x = ){\text{ }}21">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>21</mn>
</math></span> <strong><em>(A1)(G1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar C = ){\text{ }}55">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
</math></span> <strong><em>(A1)(G1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept (i) 21000 and (ii) 55000 seen.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>their mean point M labelled on diagram <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<p>Award <strong><em>(A1)</em>(ft) </strong>if their part (b) is correct and their attempt at plotting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(21,{\text{ }}55)">
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> in part (a) is labelled M.</p>
<p>If graph paper not used, award <strong><em>(A1) </em></strong>if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(21,{\text{ }}55)">
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> is labelled. If their answer from part (b) is incorrect and accuracy cannot be determined, award <strong><em>(A0)</em></strong>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}0.990{\text{ }}(0.989568 \ldots )">
<mo stretchy="false">(</mo>
<mi>r</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.990</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.989568</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(G2) </em></strong>for 0.99 seen. Award <strong><em>(G1) </em></strong>for 0.98 or 0.989. Do not accept 1.00.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the correlation coefficient/<em>r </em>is (very) close to 1 <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>the correlation is (very) strong <strong><em>(R1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their answer to part (d).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>the position of the data points on the scatter graphs suggests that the tendency is linear <strong><em>(R1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their scatter graph in part (a).</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C = 1.94x + 14.2{\text{ }}(C = 1.94097 \ldots x + 14.2395 \ldots )">
<mi>C</mi>
<mo>=</mo>
<mn>1.94</mn>
<mi>x</mi>
<mo>+</mo>
<mn>14.2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>C</mi>
<mo>=</mo>
<mn>1.94097</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>14.2395</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(G1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.94x">
<mn>1.94</mn>
<mi>x</mi>
</math></span>, <strong><em>(G1) </em></strong>for 14.2.</p>
<p>Award a maximum of <strong><em>(G0)(G1) </em></strong>if the answer is not an equation.</p>
<p>Award <strong><em>(G0)(G1)</em>(ft) </strong>if gradient and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>-intercept are swapped in the equation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>straight line through their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{M}}(21,{\text{ }}55)">
<mrow>
<mtext>M</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>-intercept of the line (or extension of line) passing through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="14.2{\text{ }}( \pm 1)">
<mn>14.2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>±</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from part (f). In the event that the regression line is not straight (ruler not used), award <strong><em>(A0)(A1)</em>(ft) </strong>if line passes through both their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(21,{\text{ }}55)">
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}14.2)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>14.2</mn>
<mo stretchy="false">)</mo>
</math></span>, otherwise award <strong><em>(A0)(A0)</em></strong>. The line must pass <em>through </em>the midpoint, not <em>near </em>this point. If it is not clear award <strong><em>(A0)</em></strong>.</p>
<p>If graph paper is not used, award at most (A1)(ft)(A0).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.99x = 1.94097 \ldots x + 14.2395 \ldots ">
<mn>2.99</mn>
<mi>x</mi>
<mo>=</mo>
<mn>1.94097</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>14.2395</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.99x">
<mn>2.99</mn>
<mi>x</mi>
</math></span> seen and <strong><em>(M1) </em></strong>for equating to their equation of the regression line. Accept an inequality sign.</p>
<p>Accept a correct graphical method involving their part (f) and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.99x">
<mn>2.99</mn>
<mi>x</mi>
</math></span>.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C = 2.99x">
<mi>C</mi>
<mo>=</mo>
<mn>2.99</mn>
<mi>x</mi>
</math></span> drawn on their scatter graph.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 13.5739 \ldots ">
<mi>x</mi>
<mo>=</mo>
<mn>13.5739</mn>
<mo>…</mo>
</math></span> (this step may be implied by their final answer) <strong><em>(A1)</em>(ft)(G2)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13\,600{\text{ }}(13\,574)">
<mn>13</mn>
<mspace width="thinmathspace"></mspace>
<mn>600</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>13</mn>
<mspace width="thinmathspace"></mspace>
<mn>574</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their answer to (f). Use of 3 sf gives an answer of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13\,524">
<mn>13</mn>
<mspace width="thinmathspace"></mspace>
<mn>524</mn>
</math></span>.</p>
<p>Award <strong><em>(G2) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{13.5739}} \ldots ">
<mrow>
<mtext>13.5739</mtext>
</mrow>
<mo>…</mo>
</math></span> or 13.524 or a value which rounds to 13500 seen without workings.</p>
<p>Award the last <strong><em>(A1)</em>(ft) </strong>for correct multiplication by 1000 <strong>and </strong>an answer satisfying revenue > <strong>their </strong>production cost.</p>
<p>Accept 13.6 thousand (folders).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A biased four-sided die is rolled. The following table gives the probability of each score.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected value of the score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is rolled 80 times. On how many rolls would you expect to obtain a three?</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of summing to 1 <em><strong>(M1)</strong></em></p>
<p><em>eg </em>0.28 + <em>k</em> + 1.5 + 0.3 = 1, 0.73 + <em>k</em> = 1</p>
<p><em>k</em> = 0.27 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into formula for E (<em>X</em>) <em><strong>(A1)</strong></em><br>eg 1 × 0.28 + 2 × <em>k</em> + 3 × 0.15 + 4 × 0.3</p>
<p>E (<em>X</em>) = 2.47 (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg np</em>, 80 × 0.15</p>
<p>12 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the hand lengths and the heights of five athletes on a sports team.</p>
<p style="text-align: center;"><img 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"></p>
<p>The relationship between <em>x</em> and <em>y</em> can be modelled by the regression line with equation <em>y</em> = <em>ax</em> + <em>b</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another athlete on this sports team has a hand length of 21.5 cm. Use the regression equation to estimate the height of this athlete.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of set up <em><strong>(M1)</strong></em></p>
<p><em>eg</em> correct value for <em>a</em> or <em>b</em> or <em>r</em> (seen in (ii)) or <em>r</em><sup>2 </sup>(= 0.973)</p>
<p>9.91044, −31.3194</p>
<p><em>a</em> = 9.91, <em>b</em> = −31.3, <em>y</em> = 9.91<em>x</em> − 31.3 <em><strong>A1A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.986417</p>
<p><em>r</em> = 0.986 <em><strong>A1 N1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <em>x</em> = 21.5 into <strong>their</strong> equation <em><strong> (M1)</strong></em></p>
<p><em>eg</em> 9.91(21.5) − 31.3</p>
<p>181.755</p>
<p>182 (cm) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A survey was conducted on a group of people. The first question asked how many pets they each own. The results are summarized in the following table.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The second question asked each member of the group to state their age and preferred pet. The data obtained is organized in the following table.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test is carried out at the 10 % significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the total number of people, from this group, who are <strong>pet owners</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the modal number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the median number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the ratio of teenagers to non-teenagers in its simplest form.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of teenagers that prefer cats.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value for this test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion for this test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>140 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>17:15 <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{17}}{{15}}">
<mfrac>
<mrow>
<mn>17</mn>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> for 85:75 or 1.13:1.</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>preferred pet is independent of “whether or not the respondent was a teenager" or "age category” <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept there is no association between pet and age. Do not accept “not related” or “not correlated” or “influenced”.</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>preferred pet is not independent of age <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (e)(i) <em>i.e.</em> award <em><strong>(A1)</strong></em><strong>(ft)</strong> if their alternative hypothesis is the negation of their null hypothesis. Accept “associated” or “dependent”.</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{85 \times 55}}{{160}}">
<mfrac>
<mrow>
<mn>85</mn>
<mo>×</mo>
<mn>55</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{85}}{{160}} \times \frac{{55}}{{160}} \times 160">
<mfrac>
<mrow>
<mn>85</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>55</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>160</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p>29.2 (29.2187…) <em><strong>(A1)(G2)</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.208 (0.208093…) <em><strong>(G2)</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.208 > 0.1 <em><strong>(R1)</strong></em></p>
<p>accept null hypothesis <strong>OR</strong> fail to reject null hypothesis <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em> for a correct comparison of their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value to the significance level, award <strong><em>(A1)</em>(ft)</strong> for the correct result from that comparison. Accept “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value > 0.1” as part of the comparison but only if their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value is explicitly seen in part (h). Follow through from their answer to part (h). Do not award <strong><em>(R0)(A1)</em></strong>.</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">i.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p>A transportation company owns 30 buses. The distance that each bus has travelled since being purchased by the company is recorded. The cumulative frequency curve for these data is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>It is known that 8 buses travelled more than <em>m</em> kilometres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance between 15000 and 20000 kilometres.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the median distance.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the interquartile range.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the percentage of buses that travelled a distance greater than the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance less than or equal to 12 000 km.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>m</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The smallest distance travelled by one of the buses was 2500 km.<br>The longest distance travelled by one of the buses was 23 000 km.</p>
<p><strong>On graph paper</strong>, draw a box-and-whisker diagram for these data. Use a scale of 2 cm to represent 5000 km.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>28 − 20 <em><strong>(A1)</strong></em></p>
<p><em><strong>Note:</strong></em> Award <em><strong>(A1)</strong></em> for 28 and 20 seen.</p>
<p>8 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>13500 <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Accept an answer in the range 13500 to 13750.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10000 <em><strong>(G1)</strong></em></p>
<p><strong>Note:</strong> Accept an answer in the range 10000 to 10250.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>16000 <em><strong>(G1)</strong></em></p>
<p><strong>Note:</strong> Accept an answer in the range 16000 to 16250.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6000 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their part (b)(ii) and (iii).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>25% <strong><em> (A1)</em></strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>11 <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>30 − 8 <strong>OR</strong> 22 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting 30 − 8 or 22 seen.</p>
<p>15750 <em><strong> (A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Accept 15750 ± 250.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct label and scale; accept “distance” or “km” for label.</p>
<p><strong><em>(A1)</em>(ft)</strong> for correct median,<br><strong><em>(A1)</em>(ft)</strong> for correct quartiles and box,<br><em><strong>(A1)</strong></em> for endpoints at 2500 and 23 000 joined to box by straight lines.<br>Accept ±250 for the median, quartiles and endpoints.<br>Follow through from their part (b).<br>The final <em><strong>(A1)</strong></em> is not awarded if the line goes through the box.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> follows a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
</div>
<div class="specification">
<p>The avocados grown on a farm have weights, in grams, that are normally distributed with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>. Avocados are categorized as small, medium, large or premium, according to their weight. The following table shows the probability an avocado grown on the farm is classified as small, medium, large or premium.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The maximum weight of a small avocado is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>106</mn><mo>.</mo><mn>2</mn></math> grams.</p>
<p>The minimum weight of a premium avocado is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>182</mn><mo>.</mo><mn>6</mn></math> grams.</p>
</div>
<div class="specification">
<p>A supermarket purchases all the avocados from the farm that weigh more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>106</mn><mo>.</mo><mn>2</mn></math> grams.</p>
</div>
<div class="specification">
<p>Find the probability that an avocado chosen at random from this purchase is categorized as</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>μ</mi><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi><mo><</mo><mi>X</mi><mo><</mo><mi>μ</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi></mrow></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>medium.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>large.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>premium.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The selling prices of the different categories of avocado at this supermarket are shown in the following table:</p>
<p><img style="float:left;" src="data:image/png;base64,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"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p>The supermarket pays the farm <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mo> </mo><mn>200</mn></math> for the avocados and assumes it will then sell them in exactly the same proportion as purchased from the farm.</p>
<p>According to this model, find the minimum number of avocados that must be sold so that the net profit for the supermarket is at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mo> </mo><mn>438</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mfrac><mrow><mi>μ</mi><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi><mo>-</mo><mi>μ</mi></mrow><mi>σ</mi></mfrac><mo><</mo><mfrac><mrow><mi>X</mi><mo>-</mo><mi>μ</mi></mrow><mi>σ</mi></mfrac><mo><</mo><mfrac><mrow><mi>μ</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi><mo>-</mo><mi>μ</mi></mrow><mi>σ</mi></mfrac></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo><</mo><mi>Z</mi><mo><</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>2</mn><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>Z</mi><mo><</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo><</mo><mi>Z</mi><mo><</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>866385</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>μ</mi><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi><mo><</mo><mi>X</mi><mo><</mo><mi>μ</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>866</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Do not award any marks for use of their answers from part (b).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>z</mi><mn>1</mn></msub><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>75068</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>z</mi><mn>2</mn></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>30468</mn><mo>…</mo></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>correct equations <em><strong>(A1)(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>106</mn><mo>.</mo><mn>2</mn><mo>-</mo><mi>μ</mi></mrow><mi>σ</mi></mfrac><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>75068</mn><mo>…</mo><mo>,</mo><mo> </mo><mo> </mo><mi>μ</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>30468</mn><mo>…</mo><mi>σ</mi><mo>=</mo><mn>182</mn><mo>.</mo><mn>6</mn></math></p>
<p>attempt to solve their equations involving z values <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>149</mn><mo>.</mo><mn>976</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mo> </mo><mi>σ</mi><mo>=</mo><mn>25</mn><mo>.</mo><mn>0051</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>150</mn><mo>,</mo><mo> </mo><mi>σ</mi><mo>=</mo><mn>25</mn><mo>.</mo><mn>0</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>new sample space is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>96</mn><mo>%</mo></math> (may be seen in (ii) or (iii)) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mtext>medium</mtext><mo>|</mo><mtext>not small</mtext></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>576</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>96</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mtext>Medium</mtext></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mtext>Large</mtext></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mtext>Premium</mtext></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to express revenue from avocados <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>6</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>29</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>96</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>243</mn><mi>n</mi></math></p>
<p>correct inequality or equation for net profit in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>6</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>29</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>3</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>96</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>1</mn><mi>n</mi><mo>-</mo><mn>200</mn><mo>≥</mo><mn>438</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>243</mn><mi>n</mi><mo>-</mo><mn>200</mn><mo>=</mo><mn>438</mn></math></p>
<p>attempt to solve the inequality <em><strong>(M1)</strong></em></p>
<p>sketch OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>513</mn><mo>.</mo><mn>274</mn><mo>.</mo><mo>.</mo><mo>.</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>514</mn></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Only award follow through in part (d) for 3 probabilities which add up to 1. FT of probabilities from c) that do not add up to 1 should only be awarded <em><strong>M</strong></em> marks, where appropriate, in d).</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Fiona walks from her house to a bus stop where she gets a bus to school. Her time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> minutes, to walk to the bus stop is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>12</mn><mo>,</mo><mo> </mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math>.</p>
<p>Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30.</p>
</div>
<div class="specification">
<p>The length of time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> minutes, of the bus journey to Fiona’s school is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>50</mn><mo>,</mo><mo> </mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math>. The probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> minutes is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>941</mn></math>.</p>
</div>
<div class="specification">
<p>If Fiona misses the first bus, there is a second bus which departs at 07:45. She must arrive at school by 08:30 to be on time. Fiona will not arrive on time if she misses both buses. The variables <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are independent.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that it will take Fiona between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> minutes and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to walk to the bus stop.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Fiona will arrive on time.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>This year, Fiona will go to school on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>183</mn></math> days.</p>
<p>Calculate the number of days Fiona is expected to arrive on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>158655</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>15</mn><mo><</mo><mi>W</mi><mo><</mo><mn>30</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>159</mn></math> <em><strong>A2 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding standardized value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>56322</mn></math></p>
<p>correct substitution using <strong>their</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-value <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>60</mn><mo>-</mo><mn>50</mn></mrow><mi>σ</mi></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>56322</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>60</mn><mo>-</mo><mn>50</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>56322</mn></mrow></mfrac><mo>=</mo><mi>σ</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>39703</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>40</mn></math> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>217221</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>B</mi><mo><</mo><mn>45</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.217</mo></math> <em><strong>A2 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid attempt to find one possible way of being on time (do not penalize incorrect use of strict inequality signs) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>≤</mo><mn>15</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo><</mo><mn>60</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo><</mo><mi>W</mi><mo>≤</mo><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo><</mo><mn>45</mn></math></p>
<p>correct calculation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>W</mi><mo>≤</mo><mn>15</mn><mo> </mo><mtext>and</mtext><mo> </mo><mi>B</mi><mo><</mo><mn>60</mn></mrow></mfenced></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>841</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>941</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>7917</mn></math></p>
<p>correct calculation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>15</mn><mo><</mo><mi>W</mi><mo>≤</mo><mn>30</mn><mo> </mo><mtext>and</mtext><mo> </mo><mi>B</mi><mo><</mo><mn>45</mn></mrow></mfenced></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>159</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>217</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>03446</mn></math></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>841</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>941</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>159</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>217</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>7917</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>03446</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>826168</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P </mtext></math>(on time) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>826</mn></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>183</mn><mo>,</mo><mo> </mo><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>826168</mn></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>183</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>826</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>151</mn><mo>.</mo><mn>188</mn></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>151</mn><mo>.</mo><mn>158</mn></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>sf </mtext></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>151</mn></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 0.5{x^4} + 3{x^2} + 2x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p> </p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b"> <mi>x</mi> <mo>=</mo> <mi>b</mi> </math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>evidence of valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 0,{\text{ }}y = 0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </math></span></p>
<p>2.73205</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2.73"> <mi>p</mi> <mo>=</mo> <mn>2.73</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.87938, 8.11721</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1.88,{\text{ }}8.12)"> <mo stretchy="false">(</mo> <mn>1.88</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>8.12</mn> <mo stretchy="false">)</mo> </math></span> <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>rate of change is 0 (do not accept decimals) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <strong><em>M1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span>, max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’,{\text{ }}x = - 1"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </math></span></p>
<p>sketch of either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’"> <msup> <mi>f</mi> <mo>′</mo> </msup> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’"> <msup> <mi>f</mi> <mo>″</mo> </msup> </math></span>, with max/min or root (respectively) <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>Substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)"> <mi>f</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5"> <mi>y</mi> <mo>=</mo> <mn>4.5</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = - 6{x^2} + 6"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mo>−</mo> <mn>6</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>6</mn> </math></span> <strong><em>A1</em></strong></p>
<p>setting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)"> <mi>f</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5"> <mi>y</mi> <mo>=</mo> <mn>4.5</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing rate of change is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’"> <msup> <mi>f</mi> <mo>′</mo> </msup> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y’,{\text{ }}f’(1)"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></span></p>
<p>rate of change is 6 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either limits or the function into formula <strong><em>(M1)</em></strong></p>
<p>involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}"> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </math></span> (accept absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</mi> </math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x"> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </math></span>)</p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int {{{( - 0.5{x^4} + 3{x^2} + 2x)}^2}{\text{d}}x,{\text{ }}\int_1^{1.88} {{f^2}} } "> <mi>π</mi> <mo>∫</mo> <mrow> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>0.5</mn> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>+</mo> <mn>3</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>1</mn> <mrow> <mn>1.88</mn> </mrow> </msubsup> <mrow> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </mrow> </mrow> </math></span></p>
<p>128.890</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 129"> <mrow> <mtext>volume</mtext> </mrow> <mo>=</mo> <mn>129</mn> </math></span> <strong><em>A2</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 7 adult men wanted to see if there was a relationship between their Body Mass Index (BMI) and their waist size. Their waist sizes, in centimetres, were recorded and their BMI calculated. The following table shows the results.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the BMI of an adult man whose waist size is 95 cm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> (or for correct <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^2}">
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> = 0.955631 seen in (ii))</p>
<p>0.141120, 11.1424</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> = 0.141, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> = 11.1 <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.977563</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> = 0.978 <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <strong>their</strong> regression equation <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.141(95) + 11.1</p>
<p>24.5488</p>
<p>24.5 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A company produces bags of sugar whose masses, in grams, can be modelled by a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>5</mn></math>. A bag of sugar is rejected for sale if its mass is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>995</mn></math> grams.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a bag selected at random is rejected.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of bags which will be rejected from a random sample of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> bags.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that a bag is not rejected, find the probability that it has a mass greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1005</mn></math> grams.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> In this question, do not penalise incorrect use of strict inequality signs.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo></math> mass of a bag of sugar</p>
<p> </p>
<p>evidence of identifying the correct area <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mrow><mi>X</mi><mo><</mo><mn>995</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0765637</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>0766</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> In this question, do not penalise incorrect use of strict inequality signs.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo></math> mass of a bag of sugar</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0766</mn><mo>×</mo><mn>100</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≈</mo><mn>8</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>66</mn></math>.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> In this question, do not penalise incorrect use of strict inequality signs.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo></math> mass of a bag of sugar</p>
<p> </p>
<p>recognition that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>1005</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>X</mi><mo>≥</mo><mn>995</mn></menclose></mrow></mfenced></math> is required <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>995</mn><mo>∩</mo><mi>X</mi><mo>></mo><mn>1005</mn></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>995</mn></mrow></mfenced></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>1005</mn></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>995</mn></mrow></mfenced></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0765637</mn><mo>…</mo></mrow><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>0765637</mn><mo>…</mo></mrow></mfrac><mfenced><mrow><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0765637</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>923436</mn><mo>…</mo></mrow></mfrac></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>0829</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces.</p>
<p>All three dice are rolled.</p>
</div>
<div class="specification">
<p>Ted plays a game using these dice. The rules are:</p>
<ul>
<li>Having a turn means to roll all three dice.</li>
<li>He wins $10 for each green face rolled and adds this to his winnings.</li>
<li>After a turn Ted can either:<br>
<ul>
<li>end the game (and keep his winnings), or</li>
<li>have another turn (and try to increase his winnings).</li>
</ul>
</li>
<li>If two or more red faces are rolled in a turn, all winnings are lost and the game ends.</li>
</ul>
</div>
<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span> ($) represents how much is added to his winnings after a turn.</p>
<p>The following table shows the distribution for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span>, where $<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> represents his winnings in the game so far.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling exactly one red face.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling two or more red faces.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ted will always have another turn if he expects an increase to his winnings.</p>
<p>Find the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> for which Ted should end the game instead of having another turn.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">valid approach to find P(one red) (M1)<br></span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_n{C_a} \times {p^a} \times {q^{n - a}}">
<msub>
<mrow>
</mrow>
<mi>n</mi>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mi>a</mi>
</msub>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>p</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>a</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\left( {n{\text{, }}p} \right)">
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3\left( {\frac{1}{3}} \right){\left( {\frac{2}{3}} \right)^2}">
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 3 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">listing all possible cases for exactly one red (may be indicated on tree diagram)</span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">P(1 red) = 0.444 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{4}{9}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>9</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> [0.444, 0.445] </span><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"> </span><em style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><strong>A1 N2</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> [3 marks] [5 maximum for parts (a.i) and (a.ii)]</span></em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">valid approach <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>eg</em> P(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X = 2">
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>) + P(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X = 3">
<mi>X</mi>
<mo>=</mo>
<mn>3</mn>
</math></span>), 1 − P(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> ≤ 1), binomcdf<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {3{\text{,}}\,\,\frac{1}{3}{\text{,}}\,\,2{\text{,}}\,\,3} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{9} + \frac{1}{{27}}">
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, 0.222 + 0.037 , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - {\left( {\frac{2}{3}} \right)^3} - \frac{4}{9}">
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mn>4</mn>
<mn>9</mn>
</mfrac>
</math></span></p>
<p>0.259259</p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">P(at least two red) = 0.259 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{7}{27}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mn>27</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> </span><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"> </span><em style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><strong>A1 N3</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks] [5 maximum for parts (a.i) and (a.ii)]</span></em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that winning $10 means rolling exactly one green <em><strong>(M1)</strong></em></p>
<p>recognition that winning $10 also means rolling at most 1 red <em><strong>(M1)</strong></em></p>
<p><em>eg</em> “cannot have 2 or more reds”</p>
<p>correct approach <strong><em>A1</em></strong></p>
<p><em>eg</em> P(1G ∩ 0R) + P(1G ∩ 1R), P(1G) − P(1G ∩ 2R),</p>
<p> “one green and two yellows or one of each colour”</p>
<p><strong>Note:</strong> Because this is a “show that” question, do not award this <strong><em>A1</em></strong> for purely numerical expressions.</p>
<p>one correct probability for their approach <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3\left( {\frac{1}{3}} \right){\left( {\frac{1}{3}} \right)^2}">
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{6}{27}}">
<mrow>
<mfrac>
<mn>6</mn>
<mn>27</mn>
</mfrac>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3\left( {\frac{1}{3}} \right){\left( {\frac{2}{3}} \right)^2}">
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{9}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>9</mn>
</mfrac>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{2}{9}}">
<mrow>
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
</mrow>
</math></span></p>
<p>correct working leading to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{27}} + \frac{6}{{27}}">
<mfrac>
<mn>3</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{12}{{27}} - \frac{3}{{27}}">
<mfrac>
<mn>12</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{9}} + \frac{2}{{9}}">
<mfrac>
<mn>1</mn>
<mrow>
<mn>9</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>2</mn>
<mrow>
<mn>9</mn>
</mrow>
</mfrac>
</math></span></p>
<p>probability = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span> <em><strong>AG N0</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[5 marks]</span></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{7}{{27}}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, 0.259 (check <em><strong>FT</strong></em> from (a)(ii)) <em><strong>A1 N1</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[1 mark]</span></em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of summing probabilities to 1 <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum { = 1} ">
<mo>∑</mo>
<mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x + y + \frac{1}{3} + \frac{2}{9} + \frac{1}{{27}} = 1">
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{7}{{27}} - \frac{9}{{27}} - \frac{6}{{27}} - \frac{1}{{27}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.148147 (0.148407 if working with <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> value to 3 sf)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{4}{{27}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.148 <em><strong>A1 N2</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[2 marks]</span></em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into the formula for expected value <em><strong>(A1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - w \cdot \frac{7}{{27}} + 10 \cdot \frac{9}{{27}} + 20 \cdot \frac{6}{{27}} + 30 \cdot \frac{1}{{27}}">
<mo>−</mo>
<mi>w</mi>
<mo>⋅</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>10</mn>
<mo>⋅</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>20</mn>
<mo>⋅</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>30</mn>
<mo>⋅</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span></p>
<p>correct critical value (accept inequality) <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> = 34.2857 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{{240}}{7}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>240</mn>
</mrow>
<mn>7</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> > 34.2857</p>
<p>$40 <em><strong>A1 N2</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The length, <em>X </em>mm, of a certain species of seashell is normally distributed with mean 25 and variance, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2}">
<mrow>
<msup>
<mi>σ<!-- σ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
<p>The probability that <em>X</em> is less than 24.15 is 0.1446.</p>
</div>
<div class="specification">
<p>A random sample of 10 seashells is collected on a beach. Let <em>Y</em> represent the number of seashells with lengths greater than 26 mm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find P(24.15 < <em>X</em> < 25).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span>, the standard deviation of <em>X</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that a seashell selected at random has a length greater than 26 mm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find E(<em>Y</em>).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that exactly three of these seashells have a length greater than 26 mm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A seashell selected at random has a length less than 26 mm.</p>
<p>Find the probability that its length is between 24.15 mm and 25 mm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to use the symmetry of the normal curve <em><strong>(M1)</strong></em></p>
<p><em>eg</em> diagram, 0.5 − 0.1446</p>
<p>P(24.15 < <em>X</em> < 25) = 0.3554 <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of inverse normal to find z score <em><strong>(M1)</strong></em></p>
<p><em>z</em> = −1.0598</p>
<p>correct substitution <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{24.15 - 25}}{\sigma } = - 1.0598">
<mfrac>
<mrow>
<mn>24.15</mn>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>1.0598</mn>
</math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span> = 0.802 <em><strong>A1 </strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P(<em>X</em> > 26) = 0.106 <em><strong> (M1)A1 </strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial probability <em><strong>(M1)</strong></em></p>
<p>E(<em>Y</em>) = 10 × 0.10621 <em><strong>(A1)</strong></em></p>
<p>= 1.06 <em><strong>A1 </strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P(<em>Y</em> = 3) <em><strong>(M1)</strong></em></p>
<p>= 0.0655 <em><strong>A1 </strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing conditional probability <em><strong>(M1)</strong></em></p>
<p>correct substitution <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.3554}}{{1 - 0.10621}}">
<mfrac>
<mrow>
<mn>0.3554</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.10621</mn>
</mrow>
</mfrac>
</math></span></p>
<p>= 0.398 <em><strong> A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p>Events <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are independent and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>3</mn><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo></math>.</p>
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>68</mn></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo>)</mo><mo>=</mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>-</mo><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>68</mn></math></p>
<p>substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>·</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo>)</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>-</mo><mtext>P</mtext><mfenced><mi>A</mi></mfenced><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mtext> </mtext><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>68</mn></mrow></mfenced></math></p>
<p>substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mi>A</mi></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>-</mo><mn>3</mn><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mtext>P</mtext><mfenced><mi>B</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>68</mn></math> (or equivalent) <em><strong>(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> The first two <em><strong>M</strong></em> marks are independent of each other.</p>
<p> </p>
<p>attempts to solve their quadratic equation <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>133</mn><mo>…</mo><mo> </mo><mfenced><mrow><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>,</mo><mo> </mo><mfrac><mn>17</mn><mn>15</mn></mfrac></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mrow></mfenced></math> <em><strong>A2</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> if both answers are given as final answers for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo></math>.</p>
<p> </p>
<p><em><strong>[6 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question proved difficult for many students. One common error was to use <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mtext>A</mtext><mo>∪</mo><mtext>B</mtext><mo>)</mo><mo>=</mo><mtext>P(A)+P(B)</mtext></math>, which simplified the problem greatly, resulting in a linear, not a quadratic equation.</p>
</div>
<br><hr><br><div class="specification">
<p>The following table below shows the marks scored by seven students on two different mathematics tests.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Let <em>L</em><sub>1</sub> be the regression line of <em>x</em> on <em>y</em>. The equation of the line <em>L</em><sub>1</sub> can be written in the form <em>x</em> = <em>ay</em> + <em>b</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and the value of <em>b</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <em>L</em><sub>2</sub> be the regression line of <em>y</em> on <em>x</em>. The lines <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> pass through the same point with coordinates (<em>p</em> , <em>q</em>).</p>
<p>Find the value of <em>p</em> and the value of <em>q</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = 1.29 and <em>b</em> = −10.4 <em><strong> A1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognising both lines pass through the mean point <em><strong> (M1)</strong></em></p>
<p><em>p</em> = 28.7, <em>q</em> = 30.3 <em><strong>A2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>
<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>
<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that Ayako avoids the trap in this wall.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span> (0.75, 75%) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{1}{4} + \frac{1}{4} \times \frac{3}{4}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times \frac{3}{4} \times \frac{1}{4}">
<mn>2</mn>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their product <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} \times \frac{3}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span> seen, and <em><strong>(M1)</strong></em> for adding their two products or multiplying their product by 2.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{8}\,\,\,\,\left( {\frac{6}{{16}},\,\,0.375,\,\,37.5{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>8</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>6</mn>
<mrow>
<mn>16</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.375</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>37.5</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a), but only if the sum of their two fractions is 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair of branches. Follow through from part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{2}{5}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correct probabilities multiplied together.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{{10}}\,\,\,\left( {0.3,\,\,30{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.3</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>30</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or part (a).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{3}{4} \times \frac{2}{5} \times \frac{3}{6}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> <strong>OR </strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} + \frac{3}{4} \times \frac{2}{5} + \frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> and <em><strong>(M1)</strong></em> for subtracting their correct probability from 1, or adding to their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} + \frac{3}{4} \times \frac{2}{5}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{93}}{{120}}\,\,\,\,\left( {\frac{{31}}{{40}},\,\,0.775,\,\,77.5{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>93</mn>
</mrow>
<mrow>
<mn>120</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>31</mn>
</mrow>
<mrow>
<mn>40</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.775</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>77.5</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6} \times 120">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
<mo>×</mo>
<mn>120</mn>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,\,\,\left( {\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,{\text{OR}}\,\,\frac{{27}}{{120}}\,\,{\text{OR}}\,\,\frac{9}{{40}}} \right)">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>OR</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mn>120</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>OR</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>9</mn>
<mrow>
<mn>40</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <em><strong>(M1)</strong></em> for multiplying by 120.</p>
<p>= 27 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> from their calculation in part (d)(ii).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The principal of a high school is concerned about the effect social media use might be having on the self-esteem of her students. She decides to survey a random sample of 9 students to gather some data. She wants the number of students in each grade in the sample to be, as far as possible, in the same proportion as the number of students in each grade in the school.</p>
</div>
<div class="specification">
<p>The number of students in each grade in the school is shown in table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>In order to select the 3 students from grade 12, the principal lists their names in alphabetical order and selects the 28<sup>th</sup>, 56<sup>th</sup> and 84<sup>th</sup> student on the list.</p>
</div>
<div class="specification">
<p>Once the principal has obtained the names of the 9 students in the random sample, she surveys each student to find out how long they used social media the previous day and measures their self-esteem using the Rosenberg scale. The Rosenberg scale is a number between 10 and 40, where a high number represents high self-esteem.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name for this type of sampling technique.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that 3 students will be selected from grade 12.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of students in each grade in the sample.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name for this type of sampling technique.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate Pearson’s product moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret the meaning of the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> in the context of the principal’s concerns.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> makes it appropriate to find the equation of a regression line.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another student at the school, Jasmine, has a self-esteem value of 29. </p>
<p>By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Stratified sampling <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There are 260 students in total <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{84}}{{260}} \times 9 = 2.91">
<mfrac>
<mrow>
<mn>84</mn>
</mrow>
<mrow>
<mn>260</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>9</mn>
<mo>=</mo>
<mn>2.91</mn>
</math></span> <em><strong>M1A1</strong></em></p>
<p>So 3 students will be selected. <em><strong>AG</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>grade 9 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{60}}{{260}} \times 9 \approx 2">
<mo>=</mo>
<mfrac>
<mrow>
<mn>60</mn>
</mrow>
<mrow>
<mn>260</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>9</mn>
<mo>≈</mo>
<mn>2</mn>
</math></span>, grade 10 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{83}}{{260}} \times 9 \approx 3">
<mo>=</mo>
<mfrac>
<mrow>
<mn>83</mn>
</mrow>
<mrow>
<mn>260</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>9</mn>
<mo>≈</mo>
<mn>3</mn>
</math></span>, grade 11 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{33}}{{260}} \times 9 \approx 1">
<mo>=</mo>
<mfrac>
<mrow>
<mn>33</mn>
</mrow>
<mrow>
<mn>260</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>9</mn>
<mo>≈</mo>
<mn>1</mn>
</math></span> <em><strong>A2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Systematic sampling <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = -0.901">
<mi>r</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.901</mn>
</math></span> <em><strong>A2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The negative value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> indicates that more time spent on social media leads to lower self-esteem, supporting the principal’s concerns. <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> being close to –1 indicates there is strong correlation, so a regression line is appropriate. <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Find the regression line of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
<mi>s</mi>
</math></span>. <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = - 0.281s + 9.74">
<mi>t</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.281</mn>
<mi>s</mi>
<mo>+</mo>
<mn>9.74</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = \left( { - 0.2807 \ldots } \right)\left( {29} \right) + 9.739 \ldots = 1.60">
<mi>t</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>0.2807</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>29</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>9.739</mn>
<mo>…</mo>
<mo>=</mo>
<mn>1.60</mn>
</math></span> hours <em><strong>M1A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A healthy human body temperature is 37.0 °C. Eight people were medically examined and the difference in their body temperature (°C), from 37.0 °C, was recorded. Their heartbeat (beats per minute) was also recorded.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a scatter diagram for temperature difference from 37 °C (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>) against heartbeat (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>). Use a scale of 2 cm for 0.1 °C on the horizontal axis, starting with −0.3 °C. Use a scale of 1 cm for 2 heartbeats per minute on the vertical axis, starting with 60 beats per minute.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean temperature difference from 37 °C, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean number of heartbeats per minute, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot and label the point M(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>) on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence describe the correlation between temperature difference from 37 °C and heartbeat.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="data:image/png;base64,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"> <em><strong>(</strong><strong>A4)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct scales, axis labels, minimum <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 0.3">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.3</mn>
</math></span>, and minimum <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 60">
<mi>y</mi>
<mo>=</mo>
<mn>60</mn>
</math></span>. Award <em><strong>(A0)</strong></em> if axes are reversed and follow through for their points.</p>
<p>Award <em><strong>(A3)</strong></em> for all eight points correctly plotted,<br><em><strong> (A2)</strong></em> for six or seven points correctly plotted.<br><em><strong> (A1)</strong></em> for four or five points correctly plotted.</p>
<p>Allow a tolerance of half a small square.</p>
<p>If graph paper has not been used, award at most <em><strong>(A1)(A0)(A0)(A0)</strong></em>.</p>
<p>If accuracy cannot be determined award <em><strong>(A0)(A0)(A0)(A0)</strong></em>.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.025 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{1}{{40}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mn>40</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>74 <strong><em>(A1)</em></strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the point M labelled, correctly plotted on their diagram <strong><em>(A1)(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for labelled M. Do not accept any other label. Award <strong><em>(A1)</em>(ft)</strong> for their point M correctly plotted. Follow through from part (b).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.807 (0.806797…) <strong><em>(G2)</em></strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(moderately) strong, positive <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for (moderately) strong, <em><strong>(A1)</strong></em> for positive. Follow through from part (d)(i). If there is no answer to part (d)(i), award at most <em><strong>(A0)</strong></em><em><strong>(A1)</strong></em>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 22.0x + 73.5\,\,\left( {y = 21.9819 \ldots x + 73.4504 \ldots } \right)">
<mi>y</mi>
<mo>=</mo>
<mn>22.0</mn>
<mi>x</mi>
<mo>+</mo>
<mn>73.5</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>=</mo>
<mn>21.9819</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>73.4504</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award<em><strong> (G1)</strong> </em>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="22.0x">
<mn>22.0</mn>
<mi>x</mi>
</math></span>, <em><strong>(G1)</strong></em> for 73.5.</p>
<p>Award a maximum of <em><strong>(G0)(G1)</strong></em> if the answer is not an equation.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>their regression line correctly drawn on scatter diagram <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a straight line, using a ruler, intercepting their mean point, and <strong><em>(A1)</em>(ft)</strong> for intercepting the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis at their 73.5 and the gradient of the line is positive. If graph paper is not used, award at most <strong><em>(A1)</em></strong><strong><em>(A0)</em></strong>. Follow through from part (e).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 66 people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>), a coach trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>) and a helicopter trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>).</p>
<p>From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3 </td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16 </td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13 </td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5 </td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x </em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8 </td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>
<div class="specification">
<p>One person in the group is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to represent the given information, using sets labelled <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n(B \cap C)">
<mi>n</mi>
<mo stretchy="false">(</mo>
<mi>B</mi>
<mo>∩</mo>
<mi>C</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person</p>
<p>(i) went on at most one trip;</p>
<p>(ii) went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-03-07_om_10.03.03.png" alt="N16/5/MATSD/SP2/ENG/TZ0/02.a/M"> <strong><em>(A5)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for rectangle and three labelled intersecting circles (U need not be seen),</p>
<p><strong><em>(A1) </em></strong>for 3 in the correct region,</p>
<p><strong><em>(A1) </em></strong>for 8 in the correct region,</p>
<p><strong><em>(A1) </em></strong>for 5, 13 and 16 in the correct regions,</p>
<p><strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2x">
<mn>2</mn>
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4x">
<mn>4</mn>
<mi>x</mi>
</math></span> in the correct regions.</p>
<p> </p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8 + 13 + 16 + 3 + 5 + x + 2x + 4x = 66">
<mn>8</mn>
<mo>+</mo>
<mn>13</mn>
<mo>+</mo>
<mn>16</mn>
<mo>+</mo>
<mn>3</mn>
<mo>+</mo>
<mn>5</mn>
<mo>+</mo>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
<mi>x</mi>
<mo>=</mo>
<mn>66</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for <strong>either </strong>a completely correct equation <strong>or </strong>adding all the terms from <strong>their </strong>diagram in part (a) and equating to 66.</p>
<p>Award <strong><em>(M0)(A0) </em></strong>if their equation has no <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7x = 66 - 45">
<mn>7</mn>
<mi>x</mi>
<mo>=</mo>
<mn>66</mn>
<mo>−</mo>
<mn>45</mn>
</math></span><strong> OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7x + 45 = 66">
<mn>7</mn>
<mi>x</mi>
<mo>+</mo>
<mn>45</mn>
<mo>=</mo>
<mn>66</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for adding their like terms correctly, <strong>but only </strong>when the solution to their equation is equal to 3 and is consistent with their original equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>The conclusion <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>15 <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a). The answer must be an integer.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{42}}{{66}}{\text{ }}\left( {\frac{7}{{11}},{\text{ }}0.636,{\text{ }}63.6\% } \right)">
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>66</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>7</mn>
<mrow>
<mn>11</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.636</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>63.6</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, <strong><em>(A1) </em></strong>for denominator. Follow through from their Venn diagram.</p>
<p> </p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{9}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333,{\text{ }}33.3\% } \right)">
<mfrac>
<mn>3</mn>
<mn>9</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.333</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>33.3</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator. Follow through from their Venn diagram.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the mean weight, <em>y</em> kg , of children who are <em>x</em> years old.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your equation to estimate the mean weight of a child that is 1.95 years old.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> correct value for <em>a</em> or <em>b</em> (or for <em>r</em> seen in (ii))</p>
<p><em>a</em> = 1.91966 <em>b</em> = 7.97717</p>
<p><em>a</em> = 1.92, <em>b</em> = 7.98 <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.984674</p>
<p><em>r </em>= 0.985 <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into their equation <em><strong>(A1)</strong></em><br><em>eg</em> 1.92 × 1.95 + 7.98</p>
<p>11.7205</p>
<p>11.7 (kg) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Ten students were surveyed about the number of hours, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, they spent browsing the Internet during week 1 of the school year. The results of the survey are given below.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\sum\limits_{i = 1}^{10} {{x_i} = 252,{\text{ }}\sigma = 5{\text{ and median}} = 27.} ">
<munderover>
<mo movablelimits="false">∑<!-- ∑ --></mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>252</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>σ<!-- σ --></mi>
<mo>=</mo>
<mn>5</mn>
<mrow>
<mtext> and median</mtext>
</mrow>
<mo>=</mo>
<mn>27.</mn>
</mrow>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean number of hours spent browsing the Internet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During week 2, the students worked on a major project and they each spent an additional five hours browsing the Internet. For week 2, write down</p>
<p>(i) the mean;</p>
<p>(ii) the standard deviation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During week 3 each student spent 5% less time browsing the Internet than during week 1. For week 3, find</p>
<p>(i) the median;</p>
<p>(ii) the variance.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>attempt to substitute into formula for mean <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Sigma x}}{{10}},{\text{ }}\frac{{252}}{n},{\text{ }}\frac{{252}}{{10}}"> <mfrac> <mrow> <mi mathvariant="normal">Σ</mi> <mi>x</mi> </mrow> <mrow> <mn>10</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>252</mn> </mrow> <mi>n</mi> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>252</mn> </mrow> <mrow> <mn>10</mn> </mrow> </mfrac> </math></span></p>
<p>mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 25.2{\text{ (hours)}}"> <mo>=</mo> <mn>25.2</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 30.2{\text{ (hours)}}"> <mo>=</mo> <mn>30.2</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N1</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = 5{\text{ (hours)}}"> <mi>σ</mi> <mo>=</mo> <mn>5</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>95%, 5% of 27</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.95 \times 27,{\text{ }}27 - (5\% {\text{ of }}27)"> <mn>0.95</mn> <mo>×</mo> <mn>27</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>27</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mn>5</mn> <mi mathvariant="normal">%</mi> <mrow> <mtext> of </mtext> </mrow> <mn>27</mn> <mo stretchy="false">)</mo> </math></span></p>
<p>median <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 25.65{\text{ (exact), }}25.7{\text{ (hours)}}"> <mo>=</mo> <mn>25.65</mn> <mrow> <mtext> (exact), </mtext> </mrow> <mn>25.7</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) <strong>METHOD 1</strong></p>
<p>variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {({\text{standard deviation}})^2}"> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mtext>standard deviation</mtext> </mrow> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> </math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid attempt to find new standard deviation <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma _{new}} = 0.95 \times 5,{\text{ }}4.75"> <mrow> <msub> <mi>σ</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>0.95</mn> <mo>×</mo> <mn>5</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>4.75</mn> </math></span></p>
<p>variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 22.5625{\text{ }}({\text{exact}}),{\text{ }}22.6"> <mo>=</mo> <mn>22.5625</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>exact</mtext> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>22.6</mn> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {({\text{standard deviation}})^2}"> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mtext>standard deviation</mtext> </mrow> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> </math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid attempt to find new variance <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{0.95^2}{\text{ }},{\text{ }}0.9025 \times {\sigma ^2}"> <mrow> <msup> <mn>0.95</mn> <mn>2</mn> </msup> </mrow> <mrow> <mtext> </mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.9025</mn> <mo>×</mo> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p>new variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 22.5625{\text{ }}({\text{exact}}),{\text{ }}22.6"> <mo>=</mo> <mn>22.5625</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>exact</mtext> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>22.6</mn> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the systolic blood pressures, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> mmHg, and the ages, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> years, of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> male patients at a medical clinic.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> can be modelled by the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mi>t</mi><mo>+</mo><mi>b</mi></math> .</p>
</div>
<div class="specification">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math>‐year‐old male patient enters the medical clinic for his appointment.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the value of Pearson’s product‐moment correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret, in context, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> found in part (a) (i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation from part (b) to predict this patient’s systolic blood pressure.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math>‐year‐old male patient enters the medical clinic for his appointment.</p>
<p>Explain why the regression equation from part (b) should not be used to predict this patient’s systolic blood pressure.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>946</mn></math> <strong>A2</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> shows a (very) strong positive correlation between age and (systolic) blood pressure <strong>A1</strong></p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>05</mn><mi>t</mi><mo>+</mo><mn>69</mn><mo>.</mo><mn>3</mn></math> <strong>A1A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Only award marks for an equation. Award <strong>A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>05</mn></math> and <strong>A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>69</mn><mo>.</mo><mn>3</mn></math>. Award <strong>A1A0</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>05</mn><mi>x</mi><mo>+</mo><mn>69</mn><mo>.</mo><mn>3</mn></math>.</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>122</mn></math> (mmHg) <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the regression equation should not be used because it involves extrapolation <strong>A1</strong></p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.</p>
</div>
<div class="specification">
<p>The participants in Group Y are 40 years or older. Their reaction times are normally distributed with mean 0.592 seconds and standard deviation <em>σ</em> seconds.</p>
</div>
<div class="specification">
<p>In the study, 38 % of the participants are in Group X.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A person is selected at random from Group X. Find the probability that their reaction time is greater than 0.65 seconds.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The probability that the reaction time of a person in Group Y is greater than 0.65 seconds is 0.396. Find the value of <em>σ</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>0.010724</p>
<p>0.0107 <em><strong>A2 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct <em>z</em>-value <em><strong>(A1)</strong></em></p>
<p>0.263714…</p>
<p>evidence of appropriate approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.65 - 0.592}}{\sigma }">
<mfrac>
<mrow>
<mn>0.65</mn>
<mo>−</mo>
<mn>0.592</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.264 = \frac{{x - u}}{\sigma }">
<mn>0.264</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mi>u</mi>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>correct substitution <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.263714 = \frac{{0.65 - 0.592}}{\sigma }">
<mn>0.263714</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.65</mn>
<mo>−</mo>
<mn>0.592</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = \frac{{0.65 - 0.592}}{{0.264}}">
<mi>σ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.65</mn>
<mo>−</mo>
<mn>0.592</mn>
</mrow>
<mrow>
<mn>0.264</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.219934</p>
<p><em>σ </em>= 0.220 <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct work for P(group X and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> > 0.65) or P(group Y and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> > 0.65) (may be seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{group X}}} \right) \times {\text{P}}\left( {t > 0.65\left| {\text{X}} \right.} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>group X</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
<mrow>
<mo>|</mo>
<mrow>
<mtext>X</mtext>
</mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{X}} \cap t > 0.65} \right) = 0.0107 \times 0.38\left( { = 0.004075} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>X</mtext>
</mrow>
<mo>∩</mo>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0107</mn>
<mo>×</mo>
<mn>0.38</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>0.004075</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>,</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{Y}} \cap t > 0.65} \right) = 0.396 \times 0.62">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>Y</mtext>
</mrow>
<mo>∩</mo>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.396</mn>
<mo>×</mo>
<mn>0.62</mn>
</math></span></p>
<p>recognizing conditional probability (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {\left. {\text{X}} \right|t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
<mrow>
<mtext>X</mtext>
</mrow>
<mo>|</mo>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {\left. A \right|B} \right) = \frac{{{\text{P}}\left( {A \cap B} \right)}}{{{\text{P}}\left( B \right)}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
<mi>A</mi>
<mo>|</mo>
</mrow>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>B</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>valid approach to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <img src="data:image/png;base64,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">, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{X and }}t > 0.65} \right) + {\text{P}}\left( {{\text{Y and }}t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>X and </mtext>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>Y and </mtext>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct work for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.0107 × 0.38 + 0.396 × 0.62, 0.249595</p>
<p>correct substitution into conditional probability formula <strong><em> A1</em></strong></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.0107 \times 0.38}}{{0.0107 \times 0.38 + 0.396 \times 0.62}}">
<mfrac>
<mrow>
<mn>0.0107</mn>
<mo>×</mo>
<mn>0.38</mn>
</mrow>
<mrow>
<mn>0.0107</mn>
<mo>×</mo>
<mn>0.38</mn>
<mo>+</mo>
<mn>0.396</mn>
<mo>×</mo>
<mn>0.62</mn>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.004075}}{{0.249595}}">
<mfrac>
<mrow>
<mn>0.004075</mn>
</mrow>
<mrow>
<mn>0.249595</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.016327</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {\left. {\text{X}} \right|t > 0.65} \right) = 0.0163270">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
<mrow>
<mtext>X</mtext>
</mrow>
<mo>|</mo>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0163270</mn>
</math></span> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial probability <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim B\left( {n,\,\,p} \right)">
<mi>X</mi>
<mo>∼</mo>
<mi>B</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{q^{n - r}}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>n</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mi>p</mi>
<mi>r</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
</math></span>, (0.016327)<sup>2</sup>(0.983672)<sup>8</sup>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {10} \\ 2 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>10</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X \geqslant 2} \right) = 1 - {\text{P}}\left( {X \leqslant 1} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>⩾</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>⩽</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - {\text{P}}\left( {X < a} \right)">
<mn>1</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo><</mo>
<mi>a</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, summing terms from 2 to 10 (accept binomcdf(10, 0.0163, 2, 10))</p>
<p>0.010994</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X \geqslant 2} \right) = 0.0110">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>⩾</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0110</mn>
</math></span> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em> </p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>SpeedWay airline flies from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span>. The flight time is normally distributed with a mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="260">
<mn>260</mn>
</math></span> minutes and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="15">
<mn>15</mn>
</math></span> minutes.</p>
<p>A flight is considered late if it takes longer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="275">
<mn>275</mn>
</math></span> minutes.</p>
</div>
<div class="specification">
<p>The flight is considered to be <strong>on time</strong> if it takes between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="275">
<mn>275</mn>
</math></span> minutes. The probability that a flight is on time is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.830">
<mn>0.830</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>During a week, SpeedWay has <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12">
<mn>12</mn>
</math></span> flights from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span>. The time taken for any flight is independent of the time taken by any other flight.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability a flight is <strong>not</strong> late.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> of these flights are <strong>on time</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> of these flights are on time, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10"> <mn>10</mn> </math></span> flights are on time.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>SpeedWay increases the number of flights from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20"> <mn>20</mn> </math></span> flights each week, and improves their efficiency so that more flights are on time. The probability that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="19"> <mn>19</mn> </math></span> flights are on time is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.788"> <mn>0.788</mn> </math></span>.</p>
<p>A flight is chosen at random. Calculate the probability that it is on time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X < 275} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mn>275</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - 0.158655"> <mn>1</mn> <mo>−</mo> <mn>0.158655</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.841344"> <mn>0.841344</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.841"> <mn>0.841</mn> </math></span> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X < 275} \right) - {\text{P}}\left( {X < m} \right) = 0.830"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mn>275</mn> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.830</mn> </math></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X < m} \right) = 0.0113447"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.0113447</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="225.820"> <mn>225.820</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="226"> <mn>226</mn> </math></span> (minutes) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of recognizing binomial distribution (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_n{C_a} \times {p^a} \times {q^{n - a}}"> <msub> <mrow> </mrow> <mi>n</mi> </msub> <mrow> <msub> <mi>C</mi> <mi>a</mi> </msub> </mrow> <mo>×</mo> <mrow> <msup> <mi>p</mi> <mi>a</mi> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mi>q</mi> <mrow> <mi>n</mi> <mo>−</mo> <mi>a</mi> </mrow> </msup> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\left( {n{\text{, }}p} \right)"> <mrow> <mtext>B</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mrow> <mtext>, </mtext> </mrow> <mi>p</mi> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>evidence of summing probabilities from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12"> <mn>12</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 7} \right) + {\text{P}}\left( {X = 8} \right) + \ldots + {\text{P}}\left( {X = 12} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>8</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mo>…</mo> <mo>+</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>12</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - {\text{P}}\left( {X \leqslant 6} \right)"> <mn>1</mn> <mo>−</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>⩽</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.991248"> <mn>0.991248</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.991"> <mn>0.991</mn> </math></span> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 10} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>10</mn> </mrow> <mo>)</mo> </mrow> </math></span> (seen anywhere) <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {12} \\ {10} \end{array}} \right) \times {0.83^{10}} \times {0.17^2}\,\,\left( { = 0.295952} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>12</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>10</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mrow> <msup> <mn>0.83</mn> <mrow> <mn>10</mn> </mrow> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mn>0.17</mn> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mn>0.295952</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>recognizing conditional probability <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A\left| B \right.} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>A</mi> <mrow> <mo>|</mo> <mi>B</mi> <mo stretchy="true" symmetric="true" fence="true"></mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 10\left| {X \geqslant 7} \right.} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>10</mn> <mrow> <mo>|</mo> <mrow> <mi>X</mi> <mo>⩾</mo> <mn>7</mn> </mrow> <mo stretchy="true" symmetric="true" fence="true"></mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}\left( {X = 10 \cap X \geqslant 7} \right)}}{{{\text{P}}\left( {X \geqslant 7} \right)}}"> <mfrac> <mrow> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>10</mn> <mo>∩</mo> <mi>X</mi> <mo>⩾</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>⩾</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.295952}}{{0.991248}}"> <mfrac> <mrow> <mn>0.295952</mn> </mrow> <mrow> <mn>0.991248</mn> </mrow> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.298565"> <mn>0.298565</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.299"> <mn>0.299</mn> </math></span> <em><strong>A1 N1</strong></em></p>
<p><strong>Note: Exception to the <em>FT</em> rule:</strong> if the candidate uses an incorrect value for the probability that a flight is on time in (i) and working shown, award full <em><strong>FT</strong></em> in (ii) as appropriate.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equation <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {20} \\ {19} \end{array}} \right){p^{19}}\left( {1 - p} \right) + {p^{20}} = 0.788"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>20</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>19</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mi>p</mi> <mrow> <mn>19</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <msup> <mi>p</mi> <mrow> <mn>20</mn> </mrow> </msup> </mrow> <mo>=</mo> <mn>0.788</mn> </math></span></p>
<p>valid attempt to solve <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.956961"> <mn>0.956961</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.957"> <mn>0.957</mn> </math></span> <em><strong>A1 N1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The mass <em>M</em> of apples in grams is normally distributed with mean <em>μ</em>. The following table shows probabilities for values of <em>M</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The apples are packed in bags of ten.</p>
<p>Any apples with a mass less than 95 g are classified as small.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <em>μ</em> = 106.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>P</em>(M < 95) .</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a bag of apples selected at random contains at most one small apple.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of bags in this crate that contain at most one small apple.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least 48 bags in this crate contain at most one small apple.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum {{p_i}} = 1">
<mo>∑</mo>
<mrow>
<mrow>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mrow>
</mrow>
<mo>=</mo>
<mn>1</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg k</em> + 0.98 + 0.01 = 1</p>
<p><em>k</em> = 0.01 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that 93 and 119 are symmetrical about <em>μ</em> <em><strong>(M1)</strong></em></p>
<p><em>eg μ</em> is midpoint of 93 and 119</p>
<p>correct working to find <em>μ</em> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{119 + 93}}{2}">
<mfrac>
<mrow>
<mn>119</mn>
<mo>+</mo>
<mn>93</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p><em>μ</em> = 106 <em><strong>AG N0</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding standardized value for 93 or 119 <em><strong> (A1)</strong></em><br><em>eg</em> <em>z</em> = −2.32634, <em>z</em> = 2.32634</p>
<p>correct substitution using <strong>their</strong> <em>z</em> value <em><strong>(A1)</strong></em><br><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{93 - 106}}{\sigma } = - 2.32634,\,\,\frac{{119 - 106}}{{2.32634}} = \sigma ">
<mfrac>
<mrow>
<mn>93</mn>
<mo>−</mo>
<mn>106</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>2.32634</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>119</mn>
<mo>−</mo>
<mn>106</mn>
</mrow>
<mrow>
<mn>2.32634</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mi>σ</mi>
</math></span></p>
<p>σ = 5.58815 <em><strong>(A1)</strong></em></p>
<p>0.024508</p>
<p>P(<em>X</em> < 95) = 0.0245 <em><strong> A2 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of recognizing binomial <strong><em>(M1) </em></strong></p>
<p><em>eg </em>10, <em>anana</em><em>Cpqn</em>−=××and 0.024B(5,,)<em>pnp</em>= </p>
<p>valid approach <strong><em>(M1) </em></strong></p>
<p><em>eg </em>P(1),P(0)P(1)<em>XXX</em>≤=+= </p>
<p>0.976285 </p>
<p>0.976 <strong><em>A1 N2 </em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing <strong>new</strong> binomial probability <em><strong>(M1)</strong></em><br><em>eg </em> B(50, 0.976)</p>
<p>correct substitution <em><strong>(A1)</strong></em><br><em>eg</em> <em>E(X) = </em>50 (0.976285)</p>
<p>48.81425</p>
<p>48.8 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> P(X ≥ 48), 1 − P(X ≤ 47)</p>
<p>0.884688</p>
<p>0.885 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two events <em>A</em> and <em>B</em> are such that P(<em>A</em>) = 0.62 and P<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {A \cap B} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩<!-- ∩ --></mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> = 0.18.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find P(<em>A</em> ∩ <em>B′ </em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P((<em>A</em> ∪ <em>B</em>)′<em> </em>) = 0.19, find P(<em>A </em>|<em> </em><em>B</em>′<em> </em>).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid approach</p>
<p><em>eg</em> Venn diagram, P(<em>A</em>) − P (<em>A</em> ∩ <em>B</em>), 0.62 − 0.18 <em><strong>(M1) </strong></em></p>
<p>P(<em>A</em> ∩ <em>B' </em>) = 0.44 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find either P(<em>B</em>′ ) or P(<em>B</em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><img src="data:image/png;base64,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"> (seen anywhere), 1 − P(<em>A</em> ∩ <em>B</em>′<em> </em>) − P((<em>A</em> ∪ <em>B</em>)′<em> </em>)</p>
<p>correct calculation for P(<em>B</em>′ ) or P(<em>B</em>) <em><strong>(A1)</strong></em></p>
<p><em>eg </em> 0.44 + 0.19, 0.81 − 0.62 + 0.18</p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}\left( {A \cap B'} \right)}}{{{\text{P}}\left( {B'} \right)}}"> <mfrac> <mrow> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>A</mi> <mo>∩</mo> <msup> <mi>B</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>B</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span> <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.44}}{{0.19 + 0.44}},\,\,\frac{{0.44}}{{1 - 0.37}}"> <mfrac> <mrow> <mn>0.44</mn> </mrow> <mrow> <mn>0.19</mn> <mo>+</mo> <mn>0.44</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>0.44</mn> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>0.37</mn> </mrow> </mfrac> </math></span></p>
<p>0.698412</p>
<p>P(<em>A </em>|<em> </em><em>B</em>′<em> </em>) = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{44}}{{63}}"> <mfrac> <mrow> <mn>44</mn> </mrow> <mrow> <mn>63</mn> </mrow> </mfrac> </math></span> (exact), 0.698 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A bakery makes two types of muffins: chocolate muffins and banana muffins.</p>
<p>The weights, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> grams, of the chocolate muffins are normally distributed with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>62</mn><mo> </mo><mtext>g</mtext></math> and standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>g</mtext></math>.</p>
</div>
<div class="specification">
<p>The weights, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> grams, of the banana muffins are normally distributed with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68</mn><mo> </mo><mtext>g</mtext></math> and standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>4</mn><mo> </mo><mtext>g</mtext></math>.</p>
<p>Each day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>%</mo></math> of the muffins made are chocolate.</p>
<p>On a particular day, a muffin is randomly selected from all those made at the bakery.</p>
</div>
<div class="specification">
<p>The machine that makes the chocolate muffins is adjusted so that the mean weight of the chocolate muffins remains the same but their standard deviation changes to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo> </mo><mtext>g</mtext></math>. The machine that makes the banana muffins is not adjusted. The probability that the weight of a randomly selected muffin from these machines is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math> is now <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>157</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected chocolate muffin weighs less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a random selection of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> chocolate muffins, find the probability that exactly <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> weigh less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the randomly selected muffin weighs less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that a randomly selected muffin weighs less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>, find the probability that it is chocolate.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>365112</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>365</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of binomial eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>12</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>365</mn><mo>…</mo></mrow></mfenced></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>213666</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>214</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>M</mi></math> represent ‘chocolate muffin’ and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>M</mi></math> represent ‘banana muffin’</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>B</mi><mo><</mo><mn>61</mn><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>0197555</mn><mo>.</mo><mo>.</mo><mo>.</mo></math><strong> <em>(A1)</em></strong></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mi>M</mi></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>C</mi><mi>M</mi></menclose></mrow></mfenced><mo>+</mo><mtext>P</mtext><mfenced><mrow><mi>B</mi><mi>M</mi></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>B</mi><mo><</mo><mn>61</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mi>M</mi></menclose></mrow></mfenced></math> (or equivalent in words)<strong> <em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p>tree diagram showing two ways to have a muffin weigh <math xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mn>61</mn></math><strong> <em>(M1)</em></strong></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>6</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>365</mn><mo>…</mo></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0197</mn><mo>…</mo></mrow></mfenced></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>226969</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>227</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing conditional probability<strong> <em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Recognition must be shown in context either in words or symbols, not just <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi></menclose></mrow></mfenced></math></p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>6</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>365112</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>226969</mn><mo>…</mo></mrow></mfrac></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>965183</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>965</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mi>M</mi></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>C</mi><mi>M</mi></menclose></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>B</mi><mi>M</mi></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>B</mi><mo><</mo><mn>61</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mi>M</mi></menclose></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>157</mn></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>6</mn><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0197555</mn><mo>…</mo></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>157</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>248496</mn><mo>…</mo></math><strong> <em>(A1)</em></strong></p>
<p>attempt to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> using GDC<strong> <em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for a graph or table of values to show their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced></math> with a variable standard deviation.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>47225</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>47</mn><mo> </mo><mfenced><mtext>g</mtext></mfenced></math><strong> <em>A2</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mi>M</mi></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>C</mi><mi>M</mi></menclose></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>B</mi><mi>M</mi></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>B</mi><mo><</mo><mn>61</mn><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mi>M</mi></menclose></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>157</mn></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>6</mn><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0197555</mn><mo>…</mo></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>157</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>248496</mn><mo>…</mo></math><strong> <em>(A1)</em></strong></p>
<p>use of inverse normal to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math> score of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>C</mi><mo><</mo><mn>61</mn></mrow></mfenced></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>679229</mn><mo>…</mo></math></p>
<p>correct substitution<strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>61</mn><mo>-</mo><mn>62</mn></mrow><mi>σ</mi></mfrac><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>679229</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>47225</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>47</mn><mo> </mo><mfenced><mtext>g</mtext></mfenced></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was common to both HL and SL papers.</p>
<p>The first two parts of this question were generally well done, with many candidates demonstrating an understanding of how to find, using their GDC, the required probability from a normal distribution in part (a), and recognising the binomial probability in part (b).</p>
<p>Parts (c) and (d) were not done well, although many that were able to make progress in part (d) were often able to give concise solutions. Most that attempted part (c) did very poorly, while few attempted part (d). Both parts proved challenging, principally due to difficulties in determining the different possible outcomes with combined events. In part (c)(i), tree diagrams were unfortunately rarely seen, as were attempts to set out the ways of selecting a muffin weighing less than 61 g, either in words, or using appropriate notation involving probabilities. Those who did understand these concepts on the other hand were much more likely to be able to find the conditional probability in part (c)(ii) and be successful in part (d). Common errors included not considering both types of muffin, and in part (d) using a probability instead of a <em>z</em>-value.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The number of messages, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M">
<mi>M</mi>
</math></span>, that six randomly selected teenagers sent during the month of October is shown in the following table. The table also shows the time, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
<mi>T</mi>
</math></span>, that they spent talking on their phone during the same month.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The relationship between the variables can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M = aT + b">
<mi>M</mi>
<mo>=</mo>
<mi>a</mi>
<mi>T</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your regression equation to predict the number of messages sent by a teenager that spent <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="154"> <mn>154</mn> </math></span> minutes talking on their phone in October.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of set up <em><strong>(M1)</strong></em></p>
<p><em>eg</em> correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 0.966856"> <mi>r</mi> <mo>=</mo> <mn>0.966856</mn> </math></span>)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4.30161"> <mn>4.30161</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="163.330"> <mn>163.330</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 4.30"> <mi>a</mi> <mo>=</mo> <mn>4.30</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 163"> <mi>b</mi> <mo>=</mo> <mn>163</mn> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.30x + 163"> <mi>y</mi> <mo>=</mo> <mn>4.30</mn> <mi>x</mi> <mo>+</mo> <mn>163</mn> </math></span>) <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4.30\left( {154} \right) + 163"> <mn>4.30</mn> <mrow> <mo>(</mo> <mrow> <mn>154</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>163</mn> </math></span></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="825.778"> <mn>825.778</mn> </math></span> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="825.2"> <mn>825.2</mn> </math></span> from 3 sf values) <em><strong>(A1)</strong></em></p>
<p>number of messages <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="= 826"> <mo>=</mo> <mn>826</mn> </math></span> (must be an integer) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A random sample of nine adults were selected to see whether sleeping well affected their reaction times to a visual stimulus. Each adult’s reaction time was measured twice.</p>
<p>The first measurement for reaction time was taken on a morning after the adult had slept well. The second measurement was taken on a morning after the same adult had not slept well.</p>
<p>The box and whisker diagrams for the reaction times, measured in seconds, are shown below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Consider the box and whisker diagram representing the reaction times after sleeping well.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the median reaction time after sleeping well.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Verify that the measurement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>46</mn></math> seconds is not an outlier.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why it appears that the mean reaction time is greater than the median reaction time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Now consider the two box and whisker diagrams.</p>
<p>Comment on whether these box and whisker diagrams provide any evidence that might suggest that not sleeping well causes an increase in reaction time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>28</mn></math> (s) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IQR</mtext><mo>=</mo><mn>0</mn><mo>.</mo><mn>35</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>27</mn><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>08</mn></mrow></mfenced></math> (s) <em><strong>(A1)</strong></em></p>
<p>substituting <strong>their</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IQR</mtext></math> into correct expression for upper fence <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>35</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>08</mn><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>47</mn></mrow></mfenced></math> (s) </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>46</mn><mo><</mo><mn>0</mn><mo>.</mo><mn>47</mn></math> <em><strong>R1</strong></em></p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>46</mn></math> (s) is not an outlier <em><strong>AG</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>the median is closer to the lower quartile (positively skewed) <em><strong>R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>The distribution is positively skewed <em><strong>R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>the range of reaction times below the median is smaller than the range of reaction times above the median <em><strong>R1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> These are sample answers from a range of acceptable correct answers. Award <em><strong>R1</strong></em> for any correct statement that explains this.<br>Do not award <em><strong>R1</strong></em> if there is also an incorrect statement, even if another statement in the answer is correct. Accept a correctly and clearly labelled diagram.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>the distribution for ‘not sleeping well’ is centred at a higher reaction time <em><strong>R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>The median reaction time after not sleeping well is equal to the upper quartile reaction time after sleeping well <em><strong>R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo>%</mo></math> of reaction times are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo><</mo><mn>0</mn><mo>.</mo><mn>35</mn></math> seconds after sleeping well, compared with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>%</mo></math> after not sleeping well <em><strong>R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>the sample size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> is too small to draw any conclusions <em><strong>R1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> These are sample answers from a range of acceptable correct answers. Accept any relevant correct statement <strong>that relates to the median and/or quartiles shown in the box plots</strong>. <strong>Do not accept</strong> a comparison of means. Do not award <em><strong>R1</strong> </em>if there is also an incorrect statement, even if another statement in the answer is correct.</p>
<p>Award <em><strong>R0</strong> </em>to “correlation does not imply causation”.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) and (b) were generally known, but answers to parts (c) and (d) showed poor understanding of interpreting data. Many students thought they could find the mean by considering only the end points. Others assumed it would be halfway between the quartiles. When it came to evidence, many were far too quick to say the diagrams 'proved' something. Most compared only the medians and thought that was sufficient evidence, completely ignoring the fact the median only represented one data point. Others just compared the maximum and minimum. A few commented correctly that 9 subjects was too small a sample to prove anything.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A six-sided biased die is weighted in such a way that the probability of obtaining a “six” is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7}{{10}}">
<mfrac>
<mn>7</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is tossed five times. Find the probability of obtaining at most three “sixes”.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is tossed five times. Find the probability of obtaining the third “six” on the fifth toss.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>recognition of binomial <em><strong>(M1)</strong></em></p>
<p><em>X</em> ~ B(5, 0.7)</p>
<p>attempt to find P (<em>X</em> ≤ 3) <em><strong>M1</strong></em></p>
<p>= 0.472 (= 0.47178) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of 2 sixes in 4 tosses <em><strong>(M1)</strong></em></p>
<p>P (3rd six on the 5th toss) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left[ {\left( {\begin{array}{*{20}{c}} 4 \\ 2 \end{array}} \right) \times {{\left( {0.7} \right)}^2} \times {{\left( {0.3} \right)}^2}} \right] \times 0.7 \left( {=0.2646 \times 0.7} \right)">
<mo>=</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.7</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.3</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
<mo>×</mo>
<mn>0.7</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>0.2646</mn>
<mo>×</mo>
<mn>0.7</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p>= 0.185 (= 0.18522) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 800 students answered 40 questions on a category of their choice out of History, Science and Literature.</p>
<p>For each student the category and the number of correct answers, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, was recorded. The results obtained are represented in the following table.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_14.11.54.png" alt="N17/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test at the 5% significance level is carried out on the results. The critical value for this test is 12.592.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span> is a discrete or a continuous variable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, the modal class;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, the mid-interval value of the modal class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis for this test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value for the test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the result of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>discrete <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11 \leqslant N \leqslant 20">
<mn>11</mn>
<mo>⩽</mo>
<mi>N</mi>
<mo>⩽</mo>
<mn>20</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>15.5 <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="21.2{\text{ }}(21.2125)">
<mn>21.2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>21.2125</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9.60{\text{ }}(9.60428 \ldots )">
<mn>9.60</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>9.60428</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G1)</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{260}}{{800}} \times \frac{{157}}{{800}} \times 800">
<mfrac>
<mrow>
<mn>260</mn>
</mrow>
<mrow>
<mn>800</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>157</mn>
</mrow>
<mrow>
<mn>800</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>800</mn>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{260 \times 157}}{{800}}">
<mfrac>
<mrow>
<mn>260</mn>
<mo>×</mo>
<mn>157</mn>
</mrow>
<mrow>
<mn>800</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into expected frequency formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 51.0{\text{ }}(51.025)">
<mo>=</mo>
<mn>51.0</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>51.025</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>choice of category and number of correct answers are independent <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Accept “no association” between (choice of) category and number of correct answers. Do not accept “not related” or “not correlated” or “influenced”.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<p> </p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.0644{\text{ }}(0.0644123 \ldots )">
<mn>0.0644</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.0644123</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11.9{\text{ }}(11.8924 \ldots )">
<mn>11.9</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>11.8924</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the null hypothesis is not rejected (the null hypothesis is accepted) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong><em>OR</em></strong></p>
<p>(choice of) category and number of correct answers are independent <strong><em>(A1)</em>(ft)</strong></p>
<p>as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11.9 < 12.592">
<mn>11.9</mn>
<mo><</mo>
<mn>12.592</mn>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.0644 > 0.05">
<mn>0.0644</mn>
<mo>></mo>
<mn>0.05</mn>
</math></span> <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(R1) </em></strong>for a correct comparison of either their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> critical value or their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value to the significance level. Award <strong><em>(A1)</em>(ft) </strong>from that comparison.</p>
<p>Follow through from part (f). Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> is normally distributed with mean, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ<!-- μ --></mi>
</math></span>. In the following diagram, the shaded region between 9 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ<!-- μ --></mi>
</math></span> represents 30% of the distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.15.49.png" alt="M17/5/MATME/SP2/ENG/TZ1/09"></p>
</div>
<div class="specification">
<p>The standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> is 2.1.</p>
</div>
<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y">
<mi>Y</mi>
</math></span> is normally distributed with mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ<!-- λ --></mi>
</math></span> and standard deviation 3.5. The events <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X > 9">
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
</math></span> are independent, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( {(X > 9) \cap (Y > 9)} \right) = 0.4">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>∩<!-- ∩ --></mo>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.4</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 9)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
</math></span>, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(Y < 13)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < \mu ) = 0.5,{\text{ }}0.5 - 0.3">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mi>μ</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.5</mn>
<mo>−</mo>
<mn>0.3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 9) = 0.2">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.2</mn>
</math></span> (exact) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = - 0.841621">
<mi>z</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.841621</mn>
</math></span> (may be seen in equation) <strong><em>(A1)</em></strong></p>
<p>valid attempt to set up an equation with <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.842 = \frac{{\mu - X}}{\sigma },{\text{ }} - 0.842 = \frac{{X - \mu }}{\sigma },{\text{ }}z = \frac{{9 - \mu }}{{2.1}}">
<mo>−</mo>
<mn>0.842</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>μ</mi>
<mo>−</mo>
<mi>X</mi>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>0.842</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>X</mi>
<mo>−</mo>
<mi>μ</mi>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>z</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>9</mn>
<mo>−</mo>
<mi>μ</mi>
</mrow>
<mrow>
<mn>2.1</mn>
</mrow>
</mfrac>
</math></span></p>
<p>10.7674</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu = 10.8">
<mi>μ</mi>
<mo>=</mo>
<mn>10.8</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X > 9) = 0.8">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.8</mn>
</math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(A) \times {\text{P}}(B)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>A</mi>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>B</mi>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.8 \times {\text{P}}(Y > 9) = 0.4">
<mn>0.8</mn>
<mo>×</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.4</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(Y > 9) = 0.5">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.5</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = 9">
<mi>λ</mi>
<mo>=</mo>
<mn>9</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(9 < Y < 13) = 0.373450">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>9</mn>
<mo><</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.373450</mn>
</math></span> (seen anywhere) <strong><em>(A2)</em></strong></p>
<p>recognizing conditional probability <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(A|B),{\text{ P}}(Y < 13|Y > 9)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>A</mi>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>B</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{0.373}}}}{{0.5}}">
<mfrac>
<mrow>
<mrow>
<mtext>0.373</mtext>
</mrow>
</mrow>
<mrow>
<mn>0.5</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.746901</p>
<p>0.747 <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A jigsaw puzzle consists of many differently shaped pieces that fit together to form a picture.</p>
<p style="text-align: center;"><img 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"></p>
<p>Jill is doing a 1000-piece jigsaw puzzle. She started by sorting the edge pieces from the interior pieces. Six times she stopped and counted how many of each type she had found. The following table indicates this information.</p>
<p style="text-align: center;"><img 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"></p>
<p>Jill models the relationship between these variables using the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to predict how many edge pieces she had found when she had sorted a <strong>total</strong> of 750 pieces.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> (ignore incorrect labels)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 6.92986">
<mi>a</mi>
<mo>=</mo>
<mn>6.92986</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 8.80769">
<mi>b</mi>
<mo>=</mo>
<mn>8.80769</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 6.93">
<mi>a</mi>
<mo>=</mo>
<mn>6.93</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 8.81">
<mi>b</mi>
<mo>=</mo>
<mn>8.81</mn>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 6.93x + 8.81">
<mi>y</mi>
<mo>=</mo>
<mn>6.93</mn>
<mi>x</mi>
<mo>+</mo>
<mn>8.81</mn>
</math></span>) <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> 750 = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x + y">
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
</math></span>, edge + interior = 750</p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em> 750 − <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = 6.9298<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 8.807 , 93.4684</p>
<p>93 (pieces) (accept 94) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Ten students were asked for the distance, in km, from their home to school. Their responses are recorded below.</p>
<p style="text-align: center;">0.3 0.4 3 3 3.5 5 7 8 8 10</p>
</div>
<div class="specification">
<p>The following box-and-whisker plot represents this data.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, find the mean distance from a student’s home to school.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>evidence of finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\sum x }}{n}"> <mfrac> <mrow> <mo>∑</mo> <mi>x</mi> </mrow> <mi>n</mi> </mfrac> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.3 + 0.4 + 3 + \ldots + 10}}{{10}}"> <mfrac> <mrow> <mn>0.3</mn> <mo>+</mo> <mn>0.4</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mo>…</mo> <mo>+</mo> <mn>10</mn> </mrow> <mrow> <mn>10</mn> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{48.2}}{{10}}"> <mfrac> <mrow> <mn>48.2</mn> </mrow> <mrow> <mn>10</mn> </mrow> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x = 4.82"> <mrow> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> <mo>=</mo> <mn>4.82</mn> </math></span> (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = 4.25 (exact) <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> Q<sub>3</sub> − Q<sub>1</sub> 3 − 8 , 3 to 8</p>
<p>IQR = 5 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A jar contains 5 red discs, 10 blue discs and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> green discs. A disc is selected at random and replaced. This process is performed four times.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that the first disc selected is red.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> be the number of red discs selected. Find the smallest value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X{\text{ }}) < 0.6">
<mrow>
<mtext>Var</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">)</mo>
<mo><</mo>
<mn>0.6</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(red)}} = \frac{5}{{15 + m}}">
<mrow>
<mtext>P(red)</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial distribution <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim B(n,{\text{ }}p)">
<mi>X</mi>
<mo>∼</mo>
<mi>B</mi>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct value for the complement of <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> (seen anywhere) <strong><em>A1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{5}{{15 + m}},{\text{ }}\frac{{10 + m}}{{15 + m}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>10</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</math></span></p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X) = np(1 - p)">
<mrow>
<mtext>Var</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>n</mi>
<mi>p</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4\left( {\frac{5}{{15 + m}}} \right)\left( {\frac{{10 + m}}{{15 + m}}} \right),{\text{ }}\frac{{20(10 + m)}}{{{{(15 + m)}^2}}} < 0.6">
<mn>4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>20</mn>
<mo stretchy="false">(</mo>
<mn>10</mn>
<mo>+</mo>
<mi>m</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo><</mo>
<mn>0.6</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m > 12.2075">
<mi>m</mi>
<mo>></mo>
<mn>12.2075</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = 13">
<mi>m</mi>
<mo>=</mo>
<mn>13</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In Lucy’s music academy, eight students took their piano diploma examination and achieved scores out of 150. For her records, Lucy decided to record the average number of hours per week each student reported practising in the weeks prior to their examination. These results are summarized in the table below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Pearson’s product-moment correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The relationship between the variables can be modelled by the regression equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>a</mi><mi>h</mi><mo>+</mo><mi>b</mi></math>. Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One of these eight students was disappointed with her result and wished she had practised more. Based on the given data, determine how her score could have been expected to alter had she practised an extra five hours per week.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of GDC to give <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>883529</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>884</mn></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Award the <em><strong>(M1)</strong></em> for any correct value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>780624</mn><mo>…</mo></math> seen in part (a) or part (b).</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>36609</mn><mo>…</mo><mo> </mo><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>64</mn><mo>.</mo><mn>5171</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>37</mn><mo> </mo><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>64</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p><strong><br></strong><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find their difference <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>36609</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>36609</mn><mo>…</mo><mfenced><mrow><mi>h</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>+</mo><mn>64</mn><mo>.</mo><mn>5171</mn><mo>…</mo><mo>-</mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>36609</mn><mo>…</mo><mi>h</mi><mo>+</mo><mn>64</mn><mo>.</mo><mn>5171</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>83045</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn><mo>.</mo><mn>83</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>.</mo><mn>85</mn><mo> </mo><mi>from</mi><mo> </mo><mn>1</mn><mo>.</mo><mn>37</mn></mrow></mfenced></math></p>
<p>the student could have expected her score to increase by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> marks. <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept an increase of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>.</mo><mn>83</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>85</mn></math>.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> has the following probability distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.34.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/04"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2|X > 0)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>total probability = 1</p>
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.475 + 2{k^2} + \frac{k}{{10}} + 6{k^2} = 1,{\text{ }}8{k^2} + 0.1k - 0.525 = 0">
<mn>0.475</mn>
<mo>+</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mi>k</mi>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>0.1</mn>
<mi>k</mi>
<mo>−</mo>
<mn>0.525</mn>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 0.25">
<mi>k</mi>
<mo>=</mo>
<mn>0.25</mn>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2) = 0.025">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.025</mn>
</math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach for finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X > 0)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - 0.475,{\text{ }}2({0.25^2}) + 0.025 + 6({0.25^2}),{\text{ }}1 - {\text{P}}(X = 0),{\text{ }}2{k^2} + \frac{k}{{10}} + 6{k^2}">
<mn>1</mn>
<mo>−</mo>
<mn>0.475</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mn>0.25</mn>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>0.025</mn>
<mo>+</mo>
<mn>6</mn>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mn>0.25</mn>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mi>k</mi>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p>correct substitution into formula for conditional probability <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.025}}{{1 - 0.475}},{\text{ }}\frac{{0.025}}{{0.525}}">
<mfrac>
<mrow>
<mn>0.025</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.475</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>0.025</mn>
</mrow>
<mrow>
<mn>0.525</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.0476190</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2|X > 0) = \frac{1}{{21}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>21</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.0476 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The maximum temperature <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
<mi>T</mi>
</math></span>, in degrees Celsius, in a park on six randomly selected days is shown in the following table. The table also shows the number of visitors, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, to the park on each of those six days.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_17.34.22.png" alt="M17/5/MATME/SP2/ENG/TZ2/02"></p>
<p>The relationship between the variables can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = aT + b">
<mi>N</mi>
<mo>=</mo>
<mi>a</mi>
<mi>T</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15 °C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of set up <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span></p>
<p>0.667315, 22.2117</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0.667,{\text{ }}b = 22.2">
<mi>a</mi>
<mo>=</mo>
<mn>0.667</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mn>22.2</mn>
</math></span> <strong><em>A1A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.922958</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 0.923">
<mi>r</mi>
<mo>=</mo>
<mn>0.923</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.667(15) + 22.2,{\text{ }}N(15)">
<mn>0.667</mn>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>22.2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>N</mi>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>32.2214 <strong><em>(A1)</em></strong></p>
<p>32 (visitors) (must be an integer) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>A data set consisting of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> test scores has mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>5</mn></math> . One test score of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> requires a second marking and is removed from the data set.</p>
<p>Find the mean of the remaining <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> test scores.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mstyle displaystyle="true"><munderover><mi mathvariant="normal">Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>16</mn></munderover></mstyle><msub><mi>x</mi><mi>i</mi></msub></mrow><mn>16</mn></mfrac><mo>=</mo><mn>14</mn><mo>.</mo><mn>5</mn></math> <strong>(M1)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1</strong> for use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>x</mi><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mi mathvariant="normal">Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mstyle><msub><mi>x</mi><mi>i</mi></msub></mrow><mi>n</mi></mfrac></math>.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><munderover><mi mathvariant="normal">Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>16</mn></munderover><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><mn>232</mn></math> <strong>(A1)</strong></p>
<p>new <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>x</mi><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><mn>232</mn><mo>-</mo><mn>9</mn></mrow><mn>15</mn></mfrac></math> <strong>(A1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>14</mn><mo>.</mo><mn>9</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>14</mn><mo>.</mo><mn>8</mn><mover><mn>6</mn><mo>¯</mo></mover><mo>,</mo><mo>=</mo><mfrac><mn>223</mn><mn>15</mn></mfrac></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Do not accept 15.</p>
<p> </p>
<p><strong>[4 marks]</strong></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly selected from the university. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> be the expected number of left-handed students in this sample.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> students are left handed;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that fewer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> students are left handed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>evidence of binomial distribution (may be seen in part (b)) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="np,{\text{ }}150 \times 0.08"> <mi>n</mi> <mi>p</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>150</mn> <mo>×</mo> <mn>0.08</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 12"> <mi>k</mi> <mo>=</mo> <mn>12</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 12} \right) = \left( {\begin{array}{*{20}{c}} {150} \\ {12} \end{array}} \right){\left( {0.08} \right)^{12}}{\left( {0.92} \right)^{138}}"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>12</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow> <mn>150</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>12</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>0.08</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mn>12</mn> </mrow> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>0.92</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mn>138</mn> </mrow> </msup> </mrow> </math></span> <strong><em>(A1)</em></strong></p>
<p>0.119231</p>
<p>probability <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.119"> <mo>=</mo> <mn>0.119</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \leqslant 11"> <mi>X</mi> <mo>⩽</mo> <mn>11</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p>0.456800</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 12) = 0.457"> <mrow> <mtext>P</mtext> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo><</mo> <mn>12</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.457</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>, has the following probability distribution:</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mi>k</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>12</mn><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>, giving a reason for your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>41</mn><mo>+</mo><mi>k</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>28</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>46</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>29</mn><mo>-</mo><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>-</mo><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>13</mn></math> (or equivalent) <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mi>k</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>12</mn><mo>=</mo><mn>0</mn></math> <em><strong>AG</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>one of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math> <em><strong>A1</strong></em></p>
<p>reasoning to reject <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mn>1</mn></mfenced><mo>=</mo><mi>k</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>28</mn><mo>≥</mo><mn>0</mn></math> therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>≠</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> <em><strong>R1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempting to use the expected value formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>41</mn><mo>+</mo><mn>1</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>3</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>28</mn></mrow></mfenced><mo>+</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>46</mn><mo>+</mo><mn>3</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>29</mn><mo>-</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>27</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1A0</strong></em> if additional values are given.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was well done in this question, with most candidates recognising that the probabilities needed to sum to 1. Many candidates also approached part (b) appropriately. While many did so by graphing the quadratic on the GDC and identifying the zeros, most solved the equation analytically. Those that used the GDC, often assumed there was only one <em>x</em>-intercept and did not investigate the relevant area of the graph in more detail. While some who found the two required values of <em>k</em> recognised that <em>k</em> = 0.2 should be rejected by referring to the original probabilities, most had lost sight of the context of the question, and were unable to give a valid reason using P(<em>X</em> = 1) to reject this solution. Those that obtained one solution in part (b), were generally able to find the expected value successfully in part (c).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> has the following probability distribution.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> which gives the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of summing probabilities to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>+</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><mi>p</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn><mo>-</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mo> </mo><mn>1</mn><mo>-</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>-</mo><mi>p</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>7</mn><mo>+</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>-</mo><mi>p</mi></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math> formula <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>3</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mo>+</mo><mn>1</mn><mo>×</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>×</mo><mi>p</mi><mo>+</mo><mn>3</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>7</mn><mo>-</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p>valid approach to find when <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math> is a maximum <em><strong>(M1)</strong></em></p>
<p>eg max on sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mi>p</mi><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>×</mo><mfenced><mrow><mo>-</mo><mn>8</mn><mi>p</mi></mrow></mfenced><mo>=</mo><mn>0</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>×</mo><mfenced><mrow><mo>-</mo><mn>8</mn></mrow></mfenced></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>125</mn></mrow></mfenced></math> (exact) (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac></math>) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>225</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>89</mn><mn>40</mn></mfrac></math> (exact), <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>23</mn></math> <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>valid method <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span>, <img src="data:image/png;base64,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">, <img src="data:image/png;base64,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"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 0.667\left( { = - \frac{2}{3}} \right)"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mo>−</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 0.667"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> </math></span>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>