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</div><h2>SL Paper 2</h2><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, \(\bar x\);</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, \(\bar C\).</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 \({\text{M}}(\bar x,{\text{ }}\bar C)\) 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, \(r\).</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 \(C\) on \(x\) 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 \(C\) on \(x\).</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 \(C\) on \(x\) 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>
<br><hr><br><div class="specification">
<p class="p1">A manufacturer produces <span class="s1">1500 </span>boxes of breakfast cereal every day.</p>
<p class="p1">The weights of these boxes are normally distributed with a mean of <span class="s1">502 </span>grams and a standard deviation of <span class="s1">2 </span>grams.</p>
</div>
<div class="specification">
<p class="p1">All boxes of cereal with a weight between <span class="s1">497.5 </span>grams and <span class="s1">505 </span>grams are sold. The manufacturer’s income from the sale of each box of cereal is <span class="s1">$2.00</span>.</p>
</div>
<div class="specification">
<p class="p1">The manufacturer recycles any box of cereal with a weight <strong>not </strong>between <span class="s1">497.5 </span>grams and <span class="s1">505 </span>grams. The manufacturer’s recycling cost is <span class="s1">$0.16 </span>per box.</p>
</div>
<div class="specification">
<p class="p1">A <strong>different </strong>manufacturer produces boxes of cereal with weights that are normally distributed with a mean of <span class="s1">350 </span>grams and a standard deviation of <span class="s1">1.8 </span>grams.</p>
<p class="p1">This manufacturer sells all boxes of cereal that are above a minimum weight, \(w\).</p>
<p class="p1">They sell <span class="s1">97% </span>of the cereal boxes produced.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">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 class="p1">(i) <span class="Apple-converted-space"> </span>Find the probability that a box of cereal, chosen at random, is sold.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>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 class="p1">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 class="p1">Calculate the value of \(w\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">As part of his IB Biology field work, Barry was asked to measure the circumference of trees, in centimetres, that were growing at different distances, in metres, from a river bank. His results are summarized in the following table.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.50.23.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether <em>distance from the river bank </em>is a continuous <strong>or </strong>discrete variable.</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><span><strong>On graph paper, </strong>draw a scatter diagram to show Barry’s results. Use a scale of 1 cm to represent 5 m on the <em>x</em>-axis and 1 cm to represent 10 cm on the <em>y</em>-axis.</span></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><span>Write down</span></p>
<p><span>(i) the mean distance, \(\bar x\), of the trees from the river bank;</span></p>
<p><span>(ii) the mean circumference, \(\bar y\), of the trees.</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><span>Plot and label the point \({\text{M}}(\bar x,{\text{ }}\bar y)\) on your graph.</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><span>Write down</span></p>
<p><span>(i) the Pearson’s product–moment correlation coefficient, \(r\), for Barry’s results;</span></p>
<p><span>(ii) the equation of the regression line \(y\) on \(x\), for Barry’s results.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the regression line \(y\) on \(x\) on your graph.</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><span><strong>Use the equation of the regression line</strong> \(y\) on \(x\) to estimate the circumference of a tree that is 40 m from the river bank.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following table shows the number of bicycles, \(x\), produced daily by a factory and their total production cost, \(y\)<span class="s1">, in US dollars (USD)</span>. The table shows data recorded over seven days.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_10.06.31.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Write down the Pearson’s product–moment correlation coefficient, \(r\), for these data.</p>
<p class="p1">(ii) Hence comment on the result.</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 class="p1">Write down the equation of the regression line \(y\) on \(x\) for these data, in the form \(y = ax + b\).</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 class="p1">Estimate the total cost, <strong>to the nearest </strong><span class="s1"><strong>USD</strong></span>, of producing \(13\)<span class="s1"> </span>bicycles on a particular day.</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 class="p1">All the bicycles that are produced are sold. The bicycles are sold for <span class="s1">304 USD </span><strong>each</strong>.</p>
<p class="p1">Explain why the factory does <strong>not </strong>make a profit when producing \(13\)<span class="s1"> </span>bicycles on a particular day.</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 class="p1">All the bicycles that are produced are sold. The bicycles are sold for <span class="s1">304 USD </span><strong>each</strong>.</p>
<p class="p1">(i) Write down an expression for the total selling price of \(x\) bicycles.</p>
<p class="p1">(ii) Write down an expression for the <strong>profit </strong>the factory makes when producing \(x\) bicycles on a particular day.</p>
<p class="p1">(iii) Find the least number of bicycles that the factory should produce, on a particular day, in order to make a profit.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the average body weight, \(x\), and the average weight of the brain, \(y\), 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 \(r\), 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 \(y\) on \(x\), in the form \(y = mx + c\).</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>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A group of candidates sat a Chemistry examination and a Physics examination. The candidates’ marks in the Chemistry examination are normally distributed with a mean of \(60\) and a standard deviation of \(12\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a diagram that shows this information.</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><span>Write down the probability that a randomly chosen candidate who sat the Chemistry examination scored at most 60 marks.</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><span>Hee Jin scored 80 marks in the Chemistry examination.</span></p>
<p><span>Find the probability that a randomly chosen candidate who sat the Chemistry examination scored <strong>more </strong>than Hee Jin.</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><span>The candidates’ marks in the Physics examination are normally distributed with a mean of \(63\) and a standard deviation of \(10\). Hee Jin also scored \(80\) marks in the Physics examination.</span></p>
<p><span>Find the probability that a randomly chosen candidate who sat the Physics examination scored <strong>less </strong>than Hee Jin.</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><span>The candidates’ marks in the Physics examination are normally distributed with a mean of \(63\) and a standard deviation of \(10\). Hee Jin also scored \(80\) marks in the Physics examination.</span></p>
<p><span>Determine whether Hee Jin’s Physics mark, <strong>compared to the other candidates</strong>, is better than her mark in Chemistry. Give a reason for your answer.</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><span>To obtain a “grade A” a candidate must be in the top \(10\% \) of the candidates who sat the Physics examination.</span></p>
<p><span>Find the minimum possible mark to obtain a “grade A”. Give your answer correct to the nearest integer.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</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>
<br><hr><br><div class="specification">
<p>In a school, all Mathematical Studies SL students were given a test. The test contained four questions, each one on a different topic from the syllabus. The quality of each response was classified as satisfactory or not satisfactory. Each student answered only three of the four questions, each on a separate answer sheet.</p>
<p>The table below shows the number of satisfactory and not satisfactory responses for each question.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.16.22.png" alt="M17/5/MATSD/SP2/ENG/TZ2/01"></p>
</div>
<div class="specification">
<p>A \({\chi ^2}\) test is carried out at the 5% significance level for the data in the table.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.815.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If the teacher chooses a response at random, find the probability that it is a response to the Calculus question;</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>If the teacher chooses a response at random, find the probability that it is a satisfactory response to the Calculus question;</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>If the teacher chooses a response at random, find the probability that it is a satisfactory response, given that it is a response to the Calculus question.</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>The teacher groups the responses by topic, and chooses two responses to the Logic question. Find the probability that both are not satisfactory.</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 the null hypothesis for this test.</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 the expected frequency of satisfactory Calculus responses is 12.</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>Write down the number of degrees of freedom for this test.</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 \({\chi ^2}\) statistic for this data.</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>State the conclusion of this \({\chi ^2}\) test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p class="p2">For each student, the number of hours spent on social media <span class="s1">(\(x\)) </span>and the number of IB Diploma points obtained <span class="s1">(\(y\)) </span>are shown in the following table.</p>
<p class="p2" 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 class="p1">Use your graphic display calculator to find</p>
</div>
<div class="specification">
<p class="p1">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 <span class="s1">3 </span>and <span class="s1">30 </span>hours on social media.</p>
<p class="p1">The equation of the regression line <span class="s1"><em>y </em></span>on <span class="s1"><em>x </em></span>for these ten female students is</p>
<p class="p1">\[y = - \frac{2}{3}x + \frac{{125}}{3}.\]</p>
<p class="p1">An eleventh girl spent <span class="s1">34 </span>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 class="p1"><span class="s1">On graph paper, draw a scatter diagram for these data. Use a scale of </span><span class="s2">2 cm </span>to represent <span class="s2">5 </span>hours on the \(x\)-axis and <span class="s2">2 cm </span>to represent <span class="s2">10 </span>points on the \(y\)-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 class="p1"><span class="s1">(i) <span class="Apple-converted-space"> \({\bar x}\)</span>, </span>the mean number of hours spent on social media;</p>
<p class="p2">(ii) <span class="Apple-converted-space"> \({\bar y}\)</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 class="p1"><span class="s1">Plot the point \((\bar x,{\text{ }}\bar y)\) </span>on your scatter diagram and label this point <span class="s2">M</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 class="p1"><span class="s1">Write down the value of \(r\), </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 class="p1">Write down the equation of the regression line \(y\) <span class="s1">on \(x\) for these eight male students.</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 class="p1">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 class="p1">Use the given equation of the regression line to estimate the number of IB Diploma <span class="s1">points that this girl obtained.</span></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 class="p1">Write down a reason why this estimate is not reliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The table below shows the scores for 12 golfers for their first two rounds in a local golf tournament.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down the mean score in Round 1.</span></p>
<p><span>(ii) Write down the standard deviation in Round 1.</span></p>
<p><span>(iii) Find the number of these golfers that had a score of more than one standard deviation above the mean in Round 1.</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><span>Write down the correlation coefficient, <em>r</em>.</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><span><span>Write down the equation of the regression line of</span><span> <em>y</em> on <em>x</em>.</span></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><span>Another golfer scored 70 in Round 1.</span></p>
<p><span>Calculate an estimate of his score in Round 2.</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><span>Another golfer scored 89 in Round 1.</span></p>
<p><span>Determine whether you can use the equation of the regression line to estimate his score in Round 2. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a mountain region there appears to be a relationship between the number of trees growing in the region and the depth of snow in winter. A set of 10 areas was chosen, and in each area the number of trees was counted and the depth of snow measured. The results are given in the table below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a study on \(100\) students there seemed to be a difference between males and females in their choice of favourite car colour. The results are given in the table below. A \(\chi^2\) test was conducted.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find </span><span><span>the mean number of trees</span><span>.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the mean depth of snow.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the standard deviation of the depth of snow.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The covariance, <em>S<sub>xy</sub></em> = 188.5.</span></p>
<p><span>Write down the product-moment correlation coefficient, <em>r</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the regression line of <em>y</em> on <em>x</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If the number of trees in an area is 55, estimate the depth of snow.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the equation of the regression line to estimate the depth of snow in an area with 100 trees.<br></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, e, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether the answer in (e)(i) is a valid estimate of the depth of snow in the area. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, e, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of male students.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the expected frequency for males, whose favourite car colour is blue, is 12.6.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is \(5.99\) at the \(5\%\) significance level.</span></p>
<p><span>Write down the null hypothesis for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, c, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is \(5.99\) at the \(5\%\) significance level.</span></p>
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, c, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is \(5.99\) at the \(5\%\) significance level.</span></p>
<p><span>Determine whether the null hypothesis should be accepted at the \(5\%\) significance level. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, c, iv.</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, \(N\), 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 \({\chi ^2}\) 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 \(N\) 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 \(N\), 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 \(N\), 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 \(N\);</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 \(N\).</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 \(p\)-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 \({\chi ^2}\) 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>
<br><hr><br><div class="specification">
<h1><span style="font-family: times new roman,times; font-size: medium;">Part A</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">100 students are asked what they had for breakfast on a particular morning.</span> <span style="font-family: times new roman,times; font-size: medium;">There were three choices: cereal (<em>X</em>) , bread (<em>Y</em>) and fruit (<em>Z</em>). It is found that</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">10 students had all three</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">17 students had bread and fruit only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">15 students had cereal and fruit only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">12 students had cereal and bread only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">13 students had only bread</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">8 students had only cereal</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">9 students had only fruit</span></p>
</div>
<div class="specification">
<h1><span style="font-family: times new roman,times; font-size: medium;">Part B</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">The same 100 students are also asked how many meals on average they have per day. The data collected is organized in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A \({\chi ^2}\) test is carried out at the 5 % level of significance.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Represent this information on a Venn diagram.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of students who had none of the three choices for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the percentage of students who had fruit for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Describe in words what the students in the set \(X \cap Y'\) had for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student had <strong>at least</strong> two of the three choices for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random. Find the probability that both students had all three choices for breakfast.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis, H<sub>0</sub>, for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the critical value for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the expected number of females that have more than 5 meals per day is 13, correct to the nearest integer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the \(\chi _{calc}^2\) for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether H<sub>0</sub> must be accepted. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The table shows the distance, in km, of eight regional railway stations from a city centre terminus and the price, in \($\), of a return ticket from each regional station to the terminus.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_09.54.14.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram for the above data. Use a scale of \(1\) cm to represent \(10\) km on the \(x\)-axis and \(1\) cm to represent \(\$10\) on the \(y\)-axis.</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><span>Use your graphic display calculator to find</span></p>
<p><span>(i) \(\bar x\), the mean of the distances;</span></p>
<p><span>(ii) \(\bar y\), the mean of the prices.</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><span>Plot and label the point \({\text{M }}(\bar x,{\text{ }}\bar y)\) on your scatter diagram.</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><span>Use your graphic display calculator to find</span></p>
<p><span>(i) the product–moment correlation coefficient, \(r\,;\)</span></p>
<p><span>(ii) the equation of the regression line \(y\) on \(x\).</span></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><span>Draw the regression line \(y\) on \(x\) on your scatter diagram.</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><span>A ninth regional station is \(76\) km from the city centre terminus.</span></p>
<p><span><span><span>Use the equation of the regression line to estimate the price of a return ticket to the city centre terminus from this regional station. </span></span><span><span><strong>Give your answer correct to the nearest </strong></span><span><span>\({\mathbf{\$ }}\).</span></span></span></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><span>Give a reason why it is valid to use your regression line to estimate the price of this return ticket.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The actual price of the return ticket is \(\$80\).</span></p>
<p><span><strong>Using your answer to part (f)</strong>, calculate the percentage error in the estimated price of the ticket.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In a debate on voting, a survey was conducted. The survey asked people’s opinion on whether or not the minimum voting age should be reduced to 16 <span class="s1">years of age. The results are shown as follows.</span></p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-21_om_06.08.52.png" alt></p>
<p class="p2">A \({\chi ^2}\) <span class="s2">test at the 1% </span>significance level was conducted. The \({\chi ^2}\) <span class="s2">critical value of the test is 9.21</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({{\text{H}}_0}\), the null hypothesis for the test;</p>
<p class="p2"><span class="s1">(ii) <span class="Apple-converted-space"> </span>\({{\text{H}}_1}\)</span>, the alternative hypothesis for the test.</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 class="p1">Write down 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 class="p1">Show that the expected frequency of those between the ages of <span class="s1">26 </span>and <span class="s1">40 </span>who oppose the reduction in the voting age is <span class="s1">21.5</span>, correct to three significant figures.</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 class="p1">Find</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the \({\chi ^2}\) statistic;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the associated \(p\)-value for the test.</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 class="p1">Determine, giving a reason, whether \({{\text{H}}_0}\) <span class="s1">should be accepted.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The seniors from Gulf High School are required to participate in exactly one after-school sport. Data were gathered from a sample of 120 students regarding their choice of sport. The following data were recorded.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">A \({\chi ^2}\) test was carried out at the 5 % significance level to analyse the relationship between gender and choice of after-school sport.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis, H<sub>0</sub>, for this test.</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><span>Find the expected value of female footballers.</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><span>Write down the number of degrees of freedom.</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><span>Write down the critical value of \(\chi ^2\), at the 5 % level of significance.</span></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><span>Use your graphic display calculator to determine the \(\chi _{calc}^2\) value.</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><span>Determine whether H<sub>0</sub> should be accepted. Justify your answer.</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><span>One student is chosen at random from the 120 students.</span></p>
<p><span>Find the probability that this student</span></p>
<p><span>(i) is male;</span></p>
<p><span>(ii) plays tennis.</span></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><span>Two students are chosen at random from the 120 students.</span></p>
<p><span>Find the probability that</span></p>
<p><span>(i) both play football;</span></p>
<p><span>(ii) neither play basketball.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Daniel grows apples and chooses at random a sample of <span class="s1">100 </span>apples from his harvest.</p>
<p class="p1">He measures the diameters of the apples to the nearest <span class="s1">cm</span>. The following table shows the distribution of the diameters.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_08.48.03.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your graphic display calculator, write down the value of</p>
<p class="p1">(i) the mean of the diameters in this sample;</p>
<p class="p1">(ii) the standard deviation of the diameters in this 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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Calculate the percentage of <strong>small </strong>apples in Daniel’s harvest.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Of the apples harvested, <span class="s1">5</span>% are <strong>large </strong>apples.</p>
<p class="p1">Find the value of \(a\).</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Find the percentage of <strong>medium </strong>apples.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">This year, Daniel estimates that he will grow <span class="s1">\({\text{100}}\,{\text{000}}\) </span>apples.</p>
<p class="p1">Estimate the number of <strong>large </strong>apples that Daniel will grow this year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">An agricultural cooperative uses three brands of fertilizer, A, B and C, on 120 different crops. The crop yields are classified as High, Medium or Low.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The data collected are organized in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The agricultural cooperative decides to conduct a chi-squared test at the 1 % significance level using the data.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the null hypothesis, H<sub>0</sub>, for the test.</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><span>Write down the number of degrees of freedom.</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><span>Write down the critical value for the test.</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><span>Show that the expected number of Medium Yield crops using Fertilizer C is 17, correct to the nearest integer.</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><span>Use your graphic display calculator to find for the data</span></p>
<p><span>(i) the \(\chi^2\) calculated value, </span><span>\(\chi _{calc}^2\)</span><span>;</span></p>
<p><span>(ii) the <em>p</em>-value.</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><span>State the conclusion of the test. Give a reason for your decision.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The number of bottles of water sold at a railway station on each day is given in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span></p>
<p><span>(i) the mean temperature;</span></p>
<p><span>(ii) the standard deviation of the temperatures.</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><span>Write down the correlation coefficient, \(r\), for the variables \(n\) and \(T\).</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><span>Comment on your value for \(r\).</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><span>The equation of the line of regression for \(n\) on \(T\) is \(n = dT - 100\).</span></p>
<p><span>(i) Write down the value of \(d\).</span></p>
<p><span>(ii) Estimate how many bottles of water will be sold when the temperature is \({19.6^ \circ }\).</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><span>On a day when the temperature was \({36^ \circ }\) Peter calculates that \(314\) bottles would be sold. Give one reason why his answer might be unreliable.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A speed camera on Peterson Road records the speed of each passing vehicle. The speeds are found to be normally distributed with a mean of \(67\,{\text{km}}\,{{\text{h}}^{ - 1}}\) and a standard deviation of \(3.4\,{\text{km}}\,{{\text{h}}^{ - 1}}\).</p>
<p>Sketch a diagram of this normal distribution and shade the region representing the probability that the speed of a vehicle is between \(60\) and \(70\,{\text{km}}\,{{\text{h}}^{ - 1}}\).</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>A vehicle on Peterson Road is chosen at random.</p>
<p>Find the probability that the speed of this vehicle is</p>
<p>(i) more than \(60\,{\text{km}}\,{{\text{h}}^{ - 1}}\);</p>
<p>(ii) less than \(70\,{\text{km}}\,{{\text{h}}^{ - 1}}\);</p>
<p>(iii) between \(60\) and \(70\,{\text{km}}\,{{\text{h}}^{ - 1}}\).</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>It is found that \(19\,\% \) of the vehicles are exceeding the speed limit of \(s\,{\text{km}}\,{{\text{h}}^{ - 1}}\).</p>
<p>Find the value of \(s\) , correct to the nearest integer.</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>There is a fine of \({\text{US}}\$ 65\) for exceeding the speed limit on Peterson Road. On a particular day the total value of fines issued was \({\text{US}}\$ 14\,820\).</p>
<p>(i) Calculate the number of fines that were issued on this day.</p>
<p>(ii) Estimate the total number of vehicles that passed the speed camera on Peterson Road on this day.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">One day the numbers of customers at three cafés, “Alan’s Diner” ( \(A\) ), “Sarah’s Snackbar” ( \(S\) ) and “Pete’s Eats” ( \(P\) ), were recorded and are given below.</span></p>
<p><br><span style="font-family: times new roman,times; font-size: medium;"> 17 were customers of Pete’s Eats only</span><br><span style="font-family: times new roman,times; font-size: medium;"> 27 were customers of Sarah’s Snackbar only</span><br><span style="font-family: times new roman,times; font-size: medium;"> 15 were customers of Alan’s Diner only</span><br><span style="font-family: times new roman,times; font-size: medium;"> 10 were customers of Pete’s Eats <strong>and</strong> Sarah’s Snackbar <strong>but not</strong> Alan’s Diner</span><br><span style="font-family: times new roman,times; font-size: medium;"> 8 were customers of Pete’s Eats <strong>and</strong> Alan’s Diner <strong>but not</strong> Sarah’s Snackbar</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Some of the customers in each café were given survey forms to complete to find out if they were satisfied with the standard of service they received.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn Diagram, using sets labelled \(A\) , \(S\) and \(P\) , that shows this information.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 48 customers of Pete’s Eats that day. Calculate the number of people who were customers of all three cafés.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 50 customers of Sarah’s Snackbar that day. Calculate the total number of people who were customers of Alan’s Diner.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of customers of Alan’s Diner that were also customers of Pete’s Eats.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(n[(S \cup P) \cap A']\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the survey forms was chosen at random, find the probability that the form showed “Dissatisfied”;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the survey forms was chosen at random, find the probability that the form showed “Satisfied” and was completed at Sarah’s Snackbar;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the survey forms was chosen at random, find the probability that the form showed “Dissatisfied”, given that it was completed at Alan’s Diner.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span> Write down the null hypothesis, \({{\text{H}}_0}\) , for the \({\chi ^2}\) test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span>Write down the number of degrees of freedom for the test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span>Using your graphic display calculator, find \({\chi ^2}_{calc}\) .<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span>State, giving a reason, the conclusion to the test.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The Brahma chicken produces eggs with weights in grams that are normally distributed about a mean of \(55{\text{ g}}\) with a standard deviation of \(7{\text{ g}}\). The eggs are classified as small, medium, large or extra large according to their weight, as shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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Luqfjr/LVOrCuylTkxtS8zfH4xnwUk2aqWWRy90TGfUTrK/MG6VP+qGLFNd3SzWHn+0ZuGf/GM4PPajdhsp6aw96bE2jql9/gspxZD4CB73//v/9sdTNOeYtnnYaeRzopAr1jpvgwxrZulPW+WCKJQaT562A8fEjjl8odZvycimmgvyJi/TcX/xwZl/uUlcoaIcWpi5snYExdAI3OiQ/jalltZfsMc3NrXqMkVDQrClD9R6USg11L4e8Q73DKMrFdg4C5taNZSAU3mfc71PZIFjTnV186wQYWbpr7qyVKypL5CZLGPs6J1KxPfj38w93noD6+OYBo5GhSemJrf1KbEjjjnVH+11RhYmhBDb0JreKjez0INK+QGyZoTMrOHPjdve1bxakqdsWurykykaFyjIxsGZNXWgW5hKRyg11GfItN2XWL4BtTZwosNwbVFq9Y25m9k2kdaq/YRi7Y+5kmOiriyJgtTS0MJSHSMeQoIqaiDjCZJ3AsE45lu1XhRyolBqqG/cK9N+zg0mWAtOi3wKzzFtYyBLopAr1nqGg1279D57TKZME/DyhqfkxZ/e6Eo3K/ITWsEU8/X24Zy9OibSlIZyaHEUXxKyXo7pqm2zrU8JYXKZiGMGpXS27j4hzqhdvh2EqBH/DcUCyY4ZPTP66nNZGEAIZzp0U04hJ/paogTKiTVTyszS++1aSczX2319GTsIS2KCFKX9nx9DnR8/JXdGHfkXN891jrpuETCS5RBCJki+XaFm5Bx1abfKfYkTU9sSyzvt/Q8WJnjc3w7EuSD8pC+x7EqPTa0qSK19GpXYhtYshv4nmd5aGj20dFkrxyTEGbXL1K1OTG3HVWHIs7CNlGKMLCImCI55pXCoQ2wd7pYL89EWtkY9WRLj2oyEHA9qN0UhJ9b61jleiRGMjXYV9FeQmLMpebiJTw9XdWEFhsqs2EYK00YP22JIqwtLnOeIMeeqk/EtAa9OdXbyfqWsmWO6k0Zb3dGrYGWed8yY1RIc8zrhUofJfYm54iPDuWNMRj+nNnq4iyaM9tiUfILk2wkNzLMcM6LVCzhm8OnOrGNG6gyxX3Hh8HZYN8f0Uyfm1xCblZflnq9n5wjp36K/PHoaOOaVwKcOsalV4x3kxNS2Fo7FLF/H9F5I2Gihz0h5GMSMkYWfpsbJ74expNm4f/8WLVDiMVKkcHH/Mo7pveFFvfL5oCT5ytjoSre5uh3WwTFn4/4/mGYirdQwrcz5zg9T5Bb90Xc6HJevd0YWJrbRV7fLzGM/YR/EplZ18zJ31Q265+CY54dLHWI34othgmQpLiufu8SZvXL3PKMrFYr36g2FFVjhh/Kdu6GmuVIUChX5qXcp7Hx6p89n5YQQ56in7v2rXBBD55O0HDP4eLHzmDZq5dmqRXJ0bKPWDcjKrxK2jeMpBo9f/78D+tvyiuKR5yiwpe/T0n54usjvMOab3c8futJmS3ulW7PQq7iSovVsWrr+09TuVeQnL3XrlG22SpphBP8syofHTB2Kt8Hd64UPHc4s/fVLN/OYWaNfWv/2Orn0GVnXemYWelB1W8xLsWAe04MGlcxSGh1uJ4S4ZXpGzwVvNCfimFNdlRO6NOFAdd4x8wqyv/128O5y4/Kzcf9+Md/sGrb7hI/kRjB43N/Oe00hPEbKFm/DdqvumMBKwIcO6eyXOxwWrtN5CySdlVm2QHkOsKlVQ5W++Bal13dip4vYsGCra57ETYNIrb7h+H8tgYYXx4eROIA2u0R3wO6S+CPP4SA36N37E3h8AY4JZIBV0aHXK487bi2KMdOF8ff5BAtYCDgmkAFAh2nifB7svwsHb7PxwbMhTw8jcgs4JpABQIfpMUHy7XC3Bzvm8CV/+S+fgGMCGQB0mCLMM0u0jKid/Vwj4AGOCWQA0CHACeCYQAYAHQKcAI4JZADQIcAJ4JhABgAdApwAjglkANAhwAmLHDNp1BYOOOCAY22PRMeMNVQAuHpAhwAngGMCGQB0CHACOCaQAUCHACeAYwIZAHQIcAI4JpABQIcAJ4BjAhkAdAhwAjgmkAFAhwAngGMCGQB0CHACOCaQAUCHACeAYwIZAHQIcAI4JpABQIcAJ6y6Y0a3zSvEb4sM8E3mdQisCqvumIQQgh29UxHYHeWBjLESOrxGZuP+/WLZ3RN8EY6JnquNzeimvoDPOjgmwaZWFTZaaHLdbwS4IPzpcGbpr1+o9aKQK8rI3SUHWx8f1YtCzt3++3IvgE2tGuRGGy10bGpbTLbkbZYbZFEL8qclHdPb2XxuG/S0YbdQ947gRWfW6LG3lXnfPNPlrxZwTCAD8KVD6oz5evv5kLmfp7/1n3+0Zt4Nn4be8NdBs8TsJI4do9fIzzkaNrrS5i4ap2EtJ6a2leyYs/Hw/ZflXwZb+sGTVrMXvVq0VsbaPXY+HfRGFiYEW+87tVKwIPEBOCYhhGBr1JMl+psLljWaodxQ3hrvOrVSsdYzHEwc862aFEfY5mGnkc+JQq5Y67yF/fnSgycdTnV1s1h7/DHYvZYQQvCX98Ox/5UJkjfOcatTZ9ns6Kdz34lK98TUtsT8/cGYeXUbtVLLoxc6pjNqz9tfHO52ldFFxf2mjX7eC/n7BMk77qqA/xgOj3FwplLMK4injdTBMekSvbHd/4rdNZwud17ikK93RmNb71TKHd35E8m3K8qhhQlxjrq1kpcxTQiZ6o/2OiO66bNtaE3eftOZhhsdYkfvVCKGFXOW0ZV+bOvTJa5n6X21kc8Va+ogdsdwbHSlAmu+2NSqoQQc22jvbmr9zAWOOdXVzbMS9pmlv+rKUrGmvkBmQl1iZplf2W9hU6vGX/bE1O5V1NEl6xvpAo5JRXnb/S42utJNT44TJG+IrPHZqBVkW9hGSlAbikk0oA6QGrzoEBtd6WZFfkIrmGK+3j6M+AJ2TNSVd87OkR0TaXLl7O3CaVDpixDbSCmGqn5MgEYIkwOVGuqbSLYUKDkxVfIc0zYGsiQKOTe1onbpaTsmfKZhcnmjoT475+7nJ6bWjOnKOibSlAaNTngCHNM/ydIPfm3XSkxJZQnHdGtM2EZK8bvXy9cXTnSITa0qSK19mkrYhtYsCptMLOk3NBa1LLClD9R6USg11L5uLYxVgxf1VTdBitL+z4+hzo+fkjujjvyLWy5wjrpuEdDPlnwlT5JTpRNT2xLLO+39DxYmeNzfzvu3w4Lwk77EVmDcy4ON7uZeOBvzVgUhJ5aVAWfVrbV2TGy+eWmeuKX6G/X289f6+PdFMSaZjfv3b9FVF4+RInkCYt0TSB8+dDhXVsNGVyrM9WEsfV+uCLlisz8XZ55a/R1RyInCzsCaq1kmviyTmNtoV0F/BYk5m5IzRuMf7rsNB6oLUqWILYZqAgtLnBeNMbGp3Y0v+M4s/WmrXIgWba+bdXbMqf7oMbIxNrWqb3aLs3JCiHPUU/f+VS6IQqEiPw1iBJqVl+WeX41yjpD+7bt/tvWADx1GEuTYryz+OiHnjzGZq53a6OEumjBOzabkEyTfThgwOssxg8X+oo7pskwdM/LGdha1ZPmbclkHx6QT7OH/d2zp+3JVRrarGJpbuctaUX79efj+C553zKmuygmBZKjQIwo5cZmBYWA5+NDhfCaRaCLY1KqLW3/L1jG9qwkbLfQZKQ+DmFHY6o5eMV3yCZI3Ehwt4uBJqdLcJzq3Y3pveFGvnD1vPiWfO8HvMfDBqjtmTENmbgSMisYdCfqC5A2xrAyMD12pQOs7lXJ9blrYP5jCuZeOwXRR6vCiQxu18uzDY0lhHbaRcismK5/jzF65e5rRlQrFe/WG4iawtGP+Q/nO3VDTXCmGUh/sfHqnz2flJDlVSskxg08XO4/pfz8xJfewUesGZOUZhhb7I6YJ5cvvDjc6nI3794v5Ztew3fK3RDMJ+lCNW5PB1uGutNM1ll4yk+cxPWhQyeRJ0eF2QgghzqhdLrAxgTeaE3HMBalSOFCdd8y8guxvvx28S2NcPiYlx+P+dt7rreExUrYa2hFMF2UW5/Ng/104EpiND54NYe7yO8OTDv3nFMLRHH0axx3rWbJAeQ7m0vz48QzmWQx/uoh9JHGra54kpkq0POq3jI4Pg9MkzcQEW4e75YJYfoBS+XTY6DZ/jlaugt79WXH3NQGOuTwTJN8OpzDYMYcv+fulrh6rokO/Vx533FCTY8x0gVTp4oBjngO3nu2nPEvU7IFUAB2mCaRKlwAcE8gAoMP0gFTpUoBjAhkAdJgikCpdBnBMIAOADgFOAMcEMgDoEOAEcEwgA4AOAU4AxwQyAOgQ4ARwTCADgA4BTljkmImjtnDAAQcc63okOmasoQLA1QM6BDgBHBPIAKBDgBPAMYEMADoEOAEcE8gAoEOAE8AxgQwAOgQ4ARwTyACgQ4ATwDGBDAA6BDgBHBPIAKBDgBPAMYEMADoEOAEcE8gAoEOAE8AxgQwAOgQ4YdUdk90eL3psXNXO8exmfjlRyJ1v02dgBXQIrAqr7piEELpzadQfbUP75+5SjjkbD99/ubzBOaN2uVBs9tPY6HntWA0dXiN43N/Ob7b16Vkn2iZ61q41YV/JJNbWMQmxPwyGSzimM2o3eymEhNjoSoWijGBHlQuwGjo8H+H0qCijv0ytGmQqhapmYEJCGUxy7rKcY2IbKUUh9/134p3LukJvfmaNHns7wvdNh68QY00dE5tvXi6liamubqaTRINjXoLV0OH5mY3794uBORLiHHVrpTlHOzG1exXlMJXdILGpVZMdE48/DL9c2kxt1MpHSmT+Z8TOp4PeyMKEYOt9p1bi7ZZZT8ecjfudnquJ8BI99X6XeQXZ33R1k13kbcdEz9XGDeWt8a5TKxVrPcPBBFv6vrczX1kZJG3Ld6Zjxl+HZklS6/D3j4/qxXyza9iE2OZhJ2ERxo75pl0riUJOzNfbh6aTwv/f9bMaOrwIc7LBplYVStv9r8xvfYLknbSiwoWOOdVVOe5bx4PmTvv5cLl4ENvo5z00jn//+I/h8BgHZyrFvIJ42kh9fRwzsqaxmrANrVkUpF00xsQ2tJ1qYEMnprblxZiet+brndHY1juVckd3/ja1Lbc6Sdf/pID0DMc8ibuOnyWVGo/eW/aoXf6xrX+zkVIsP0DWzHvnnqET7Oi/tB69tzAhBDtGr5G/su7W92U1dHghTkxtS2Rdg2brrMxs1NpMrZeY7JjY0TuVpG+ZqCtLoiC1tFfMTuixzCzzK7uQY1Orxt81J6Z2r6KOuFr118cxWe+wDe1hL/SLn+rqpihILXWvpR0xvyHWMYlrmqFF78TUtjwfjJwceRNLOGbMdahpsm9+guSN4Do2agX1qZjyEG9JzcVYDR1ejKh63ZTWdy5so727ftoe5B+5Yq3zNpKpMLdAUpriOeafZl+pCDnRTWuoXXq6Soj7sKUP1HpRKDXUZ0vvgX5ias1wyEwIIcQxkaY0Uio1pMh6OmZcHROPkSKJ+fuDMbtCnumYlJmlv36h1osLqu9L1THnr7OMY3o1IBu18t+7Zn89rIYOL0hIOdhGD1vqXjXU+fFT8qn+aK8zoiZjG1qzmFeQfeplKr6KcHKaQm+WO9vqrx+tGcFfB80gbVpc4gygxat8oSJrZ/smNrqbe+Ebyk+tFpa5rok1dcwYnFG79o+WX510OdsxsfW+U7vTUH99qf9hXCDGxObLAxMnXmfeMQke97dv0JV/ZqEHQaLEuudqsRo6vChsYj5BykM0/Rwk5mxKHtNRcZUTvgUWpCkRWwzVBJZ1TMqp3r6RE4XcLVU/TT4Lm9rd+DBiZulPW+XCXBBzzayzY2Ln0zudeh8eo3//NBjPsHW4W77JtB3PckxsdKWbnkldICvHjv6kjSbJ14lxTEJsY1/d/ackCjmxLPd0P3GhWbnU2h95X5r+hn7na42+EKuhwwsTCNhGuwqyqUKEra75N5OSYxspxQT5neWYwUKbgmOeI8Y8MbWdBaHMUrHO1bK2jjmzRo+3FWQTmo/f879LeytybbcAAAJHSURBVJENt3/iK+bbbwfvxnjOMW3UyhdocRpbo54siXnl7ef3MRMYdII95JgzS3/akvaQjZOv8/ecY2JH/3k7PpAMF5uEnCgsM7ScAVZDhxfHXW4Pj9HD3SBmLFS14dsgJaeLa7yjRW6BxDTlco557jpmTEo+/8Fvg2NeIWc/JUmXa6+YzeY1kmZigq3D3XJBLD9A//u7d6mNSrnu6YYKjo7yGGOkFAWp1TfC3b24ed3o4G7sdT7p9L0JhR/Kd+7OTyx7s2xM8d7LZWC6aKWgzvVjo/aT6y9U2LfvVDbDTfN8OO1wjpD+jcQ2P+PTlIs55rl65cyPJabkzCe6AVk5cCno2FDSAPBqAjqkE3JMjjI33E6IN/LBCKPc0R3f7ILOz4I0JRyozjvmRgv96Xx6g0Iudq55TJ+YlByP+9t5r6yEx0jZaoRmV64fcMzMYRv9Z8PwMo7Hb3rLPPGZWUCHMflp7GgE8xyEN13EtJ5dh01KU/528y03A/vMnLbVNU/ceRJ3cjmNT9T8WY+YrPtQE33/6kDnbbgIHDNj0LmQUBpFHBMd8KesVAEdpkrqacrxoHYzse5U61upvvvrBRwza2BLP3jiViqFnFiWu2hFipULAB2myjqmKWkBjglkANBheqxpmpIW4JhABgAdpslapilpAY4JZADQIcAJ4JhABgAdApwAjglkANAhwAngmEAGAB0CnACOCWQA0CHACYscM3EkFQ444IBjXY9ExwQAAAAWA44JAACwLOCYAAAAywKOCQAAsCz/H15UCtuYEAEyAAAAAElFTkSuQmCC" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show clearly the boundaries for the classification of the eggs.</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><span>An egg is chosen at random. Find the probability that the egg is</span><br><span>(i) medium;</span><br><span>(ii) extra large.</span></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><span>There is a probability of \(0.3\) that a randomly chosen egg weighs more than \(w\) grams.</span></p>
<p><span>Find \(w\) .</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><span>The probability that a Brahma chicken produces a large size egg is \(0.121\). Frank’s Brahma chickens produce \(2000\) eggs each month.</span></p>
<p><span>Calculate an estimate of the number of large size eggs produced by Frank’s chickens each month.</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><span>The selling price, in US dollars (USD), of each size is shown in the table below.</span><br><span><img src="data:image/png;base64,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" alt></span><br><span>The probability that a Brahma chicken produces a small size egg is \(0.388\).</span></p>
<p><span>Estimate the monthly income, in USD, earned by selling the \(2000\) eggs. Give your answer correct to two decimal places.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Alex and Kris are riding their bicycles together along a bicycle trail and note the following distance markers at the given times.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram of the data. Use 1 cm to represent 1 hour and 1 cm to represent 10 km.</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><span>Write down for this set of data </span><span>the mean time, \(\bar t\).</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><span>Write down for this set of data the mean distance, \(\bar d\).</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><span>Mark and label the point \(M(\bar t,{\text{ }}\bar d)\) on your scatter diagram.</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><span>Draw the line of best fit on your scatter diagram.</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><span><strong>Using your graph</strong>, estimate the time when Alex and Kris pass the 85 km distance marker. Give your answer correct to <strong>one decimal place</strong>.</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><span>Write down the equation of the regression line for the data given.</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><span><strong>Using your equation</strong> calculate the distance marker passed by the cyclists at 10.3 hours.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Is this estimate of the distance reliable? Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A store recorded their sales of televisions during the 2010 football World Cup. They looked at the numbers of televisions bought by gender and the size of the television screens.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">This information is shown in the table below; S represents the size of the television screen in inches.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The store wants to use this information to predict the probability of selling these sizes of televisions for the 2014 football World Cup.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the table to find the probability that</span></p>
<p><span>(i) a television will be bought by a female;</span></p>
<p><span>(ii) a television with a screen size of 32 < <em>S</em> ≤ 46 will be bought;</span></p>
<p><span>(iii) a television with a screen size of 32 < <em>S</em> ≤ 46 will be bought by a female;</span></p>
<p><span>(iv) a television with a screen size greater than 46 inches will be bought, given that it is bought by a male.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong></strong>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></p>
<p><span>Write down the null hypothesis.</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><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Show that the expected frequency for females who bought a screen size of 32 < <em>S</em> ≤ 46, is 79, correct to the nearest integer.</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><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Write down the number of degrees of freedom.</span></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><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Write down the \({\chi ^2}\) calculated value.</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><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Write down the critical value for this test.</span></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><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Determine if the null hypothesis should be accepted. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Pam has collected data from a group of 400 IB Diploma students about the Mathematics course they studied and the language in which they were examined (English, Spanish or French). The summary of her data is given below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A student is chosen at random from the group. Find the probability that the student</span></p>
<p><span>(i) studied Mathematics HL;</span></p>
<p><span>(ii) was examined in French;</span></p>
<p><span>(iii) studied Mathematics HL and was examined in French;</span></p>
<p><span>(iv) did not study Mathematics SL and was not examined in English;</span></p>
<p><span>(v) studied Mathematical Studies SL given that the student was examined in Spanish.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Pam believes that the Mathematics course a student chooses is independent of the language in which the student is examined.</span></p>
<p><span>Using your answers to parts (a) (i), (ii) and (iii) above, state whether there is any evidence for Pam’s belief. Give a reason for your answer.</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><span>Pam decides to test her belief using a Chi-squared test at the \(5\% \) level of significance.</span></p>
<p><span>(i) State the null hypothesis for this test.</span></p>
<p><span>(ii) Show that the expected number of Mathematical Studies SL students who took the examination in Spanish is \(41.3\), correct to 3 significant figures.</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><span>Write down</span></p>
<p><span>(i) the Chi-squared calculated value;</span></p>
<p><span>(ii) the number of degrees of freedom;</span></p>
<p><span>(iii) the Chi-squared critical value.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State, giving a reason, whether there is sufficient evidence at the \(5\% \) level of significance that Pam’s belief is correct.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Jorge conducted a survey of \(200\) drivers. He asked two questions:</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">How long have you had your driving licence?</span><br><span style="font-family: times new roman,times; font-size: medium;">Do you wear a seat belt when driving?</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The replies are summarized in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Jorge applies a \({\chi ^2}\) test at the \(5\% \) level to investigate whether wearing a seat belt is associated with the time a driver has had their licence.</span></p>
<p><span>(i) Write down the null hypothesis, \({{\text{H}}_0}\).</span></p>
<p><span>(ii) Write down the number of degrees of freedom.</span></p>
<p><span>(iii) Show that the expected number of drivers that wear a seat belt and have had their driving licence for more than \(15\) years is \(22\), correct to the nearest whole number.</span></p>
<p><span>(iv) Write down the \({\chi ^2}\) test statistic for this data.</span></p>
<p><span>(v) Does Jorge accept \({{\text{H}}_0}\) ? Give a reason for your answer.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the \(200\) drivers surveyed. One driver is chosen at random. Calculate the probability that</span></p>
<p><span>(i) this driver wears a seat belt;</span></p>
<p><span>(ii) the driver does not wear a seat belt, <strong>given that</strong> the driver has held a licence for more than \(15\) years.</span></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><span>Two drivers are chosen at random. Calculate the probability that</span></p>
<p><span>(i) both wear a seat belt.</span></p>
<p><span>(ii) at least one wears a seat belt.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The figure below shows the lengths in centimetres of fish found in the net of a small trawler.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total number of fish in the net.</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><span>Find (i) the modal length interval,</span></p>
<p><span>(ii) the interval containing the median length,</span></p>
<p><span>(iii) an estimate of the mean length.</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><span>(i) Write down an estimate for the standard deviation of the lengths.</span></p>
<p><span>(ii) How many fish (if any) have length <strong>greater than</strong> three standard deviations <strong>above</strong> the mean?</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><span>The fishing company must pay a fine if more than 10% of the catch have lengths less than 40cm.</span></p>
<p><span>Do a calculation to decide whether the company is fined.</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><span>A sample of 15 of the fish was weighed. The weight, <em>W</em> was plotted against length, <em>L</em> as shown below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Exactly <strong>two</strong> of the following statements about the plot could be correct. Identify the two correct statements. </span></p>
<p><span><strong>Note:</strong> You do <strong>not</strong> need to enter data in a GDC <strong>or</strong> to calculate <em>r</em> exactly.</span></p>
<p><span>(i) The value of <em>r</em>, the correlation coefficient, is approximately 0.871.</span></p>
<p><span>(ii) There is an exact linear relation between <em>W</em> and <em>L</em>.</span></p>
<p><span>(iii) The line of regression of <em>W</em> on <em>L</em> has equation <em>W</em> = 0.012<em>L</em> + 0.008 .</span></p>
<p><span>(iv) There is negative correlation between the length and weight.</span></p>
<p><span>(v) The value of <em>r</em>, the correlation coefficient, is approximately 0.998.</span></p>
<p><span>(vi) The line of regression of <em>W</em> on <em>L</em> has equation <em>W</em> = 63.5<em>L</em> + 16.5.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A random sample of 167 people who own mobile phones was used to collect data on the amount of time they spent per day using their phones. The results are displayed in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Manuel conducts a survey on a random sample of 751 people to see which television programme type they watch most from the following: Drama, Comedy, Film, News. The results are as follows.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Manuel decides to ignore the ages and to test at the 5 % level of significance whether the most watched programme type is independent of <strong>gender.</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the modal group.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to calculate approximate values of the mean and standard deviation of the time spent per day on these mobile phones.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On graph paper, draw a fully labelled histogram to represent the data.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a table with 2 rows and 4 columns of data so that Manuel can perform a chi-squared test.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State Manuel’s null hypothesis and alternative hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched programme type. Give your answer to the nearest whole number.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphic display calculator, or otherwise, find the chi-squared statistic for Manuel’s data.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) State the number of degrees of freedom available for this calculation.</span></p>
<p><span>(ii) State his conclusion.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Francesca is a chef in a restaurant. She cooks eight chickens and records their masses and cooking times. The mass <em>m</em> of each chicken, in kg, and its cooking time <em>t</em>, in minutes, are shown in the following table.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the relationship between the mass of a chicken and its cooking time. Use 2 cm to represent 0.5 kg on the horizontal axis and 1 cm to represent 10 minutes on the vertical axis.</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><span>Write down for this set of data</span></p>
<p><span>(i) the mean mass, \(\bar m\) ;</span></p>
<p><span>(ii) the mean cooking time, </span><span><span>\(\bar t\)</span> .</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><span>Label the point \({\text{M}}(\bar m,\bar t)\) on the scatter diagram.</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><span>Draw the line of best fit on the scatter diagram.</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><span>Using your line of best fit, estimate the cooking time, in minutes, for a 1.7 kg chicken.</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><span>Write down the Pearson’s product–moment correlation coefficient, <em>r</em> .</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><span>Using your value for <em>r</em> , comment on the correlation.</span></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><span>The cooking time of an additional 2.0 kg chicken is recorded. If the mass and cooking time of this chicken is included in the data, the correlation is weak.</span></p>
<p><span>(i) Explain how the cooking time of this additional chicken might differ from that of the other eight chickens.</span></p>
<p><span>(ii) Explain how a new line of best fit might differ from that drawn in part (d).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A survey of \(400\) people is carried out by a market research organization in two different cities, Buenos Aires and Montevideo. The people are asked which brand of cereal they prefer out of Chocos, Zucos or Fruti. The table below summarizes their responses.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following table shows the cost in \({\text{AUD}}\) of seven paperback books chosen at random, together with the number of pages in each book.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One person is chosen at random from those surveyed. Find the probability that this person</span></p>
<p><span>(i) does not prefer Zucos;</span></p>
<p><span>(ii) prefers Chocos, given that they live in Montevideo.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two people are chosen at random from those surveyed. Find the probability that they both prefer Fruti.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>State the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>State the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>Show that the expected frequency for the number of people who live in Montevideo and prefer Zucos is \(63\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>Write down the chi-squared statistic for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>State whether the market research organization would accept the null hypothesis. Clearly justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Plot these pairs of values on a scatter diagram. Use a scale of \(1{\text{ cm}}\) to represent \(50\) pages on the horizontal axis and </span><span><span>\(1{\text{ cm}}\)</span> to represent \(1{\text{ AUD}}\) on the vertical axis.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the linear correlation coefficient, \(r\), for the data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Stephen wishes to buy a paperback book which has \(350\) pages in it. He plans to draw a line of best fit to determine the price. State whether or not this is an appropriate method in this case and justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A university required all Science students to study one language for one year. A survey was carried out at the university amongst the 150 Science students. These students all studied one of either French, Spanish or Russian. The results of the survey are shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Ludmila decides to use the \({\chi ^2}\) test at the \(5\% \) level of significance to determine whether the choice of language is independent of gender.</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">At the end of the year, only seven of the female Science students sat examinations in Science and French. The marks for these seven students are shown in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State Ludmila’s null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected frequency for the females studying Spanish.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the \({\chi ^2}\) test statistic for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether Ludmila accepts the null hypothesis. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a labelled scatter diagram for this data. Use a scale of \(2{\text{ cm}}\) to represent \(10{\text{ marks}}\) on the \(x\)-axis (\(S\)) and \(10{\text{ marks}}\) on the \(y\)-axis (\(F\)).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic calculator to find</span></p>
<p><span></span></p>
<p><span>(i) \({\bar S}\), the mean of \(S\) ;</span></p>
<p><span>(ii) \({\bar F}\), the mean of \(F\) .</span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Plot the point \({\text{M}}(\bar S{\text{, }}\bar F)\) on your scatter diagram.</span></p>
<p><span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the equation of the regression line of \(F\) on \(S\) .</span></p>
<p><span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the regression line on your scatter diagram.</span></p>
<p><span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Carletta’s mark on the Science examination was \(44\). She did not sit the French examination. </span></p>
<p><span>Estimate Carletta’s mark for the French examination.</span></p>
<p><span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span></span><span>Monique’s mark on the Science examination was 85. She did not sit the French examination. Her French teacher wants to use the regression line to estimate Monique’s mark.</span></p>
<p><span> State whether the mark obtained from the regression line for Monique’s French examination is reliable. Justify your answer.</span></p>
<p><span></span></p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">B.g.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an ecological study, Ernesto measured the average concentration \((y)\) of the fine dust, \({\text{PM}}10\), in the air at different distances \((x)\) from a power plant. His data are represented on the following scatter diagram. The concentration of \({\text{PM}}10\) is measured in micrograms per cubic metre and the distance is measured in kilometres.</p>
<p><img 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" alt></p>
<p>His data are also listed in the following table.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAr4AAABwCAYAAAD4+nOYAAAgAElEQVR4Ae2dCVgUV9b3/9Ofn/HtIJ+oE4lJFAQkoKi0Oq/bKCpjJDqCS0w0RDGiiTEKaNTMKFFDllFHWXRmTMQASsy4sCXmMzGo6LgkUdoFl7AJ4iu2iQaCpGMMdr3PrV6o7q5e2Kvbw/PwdPWtW/ee8ztV1adunXvu7ziO40B/RIAIEAEiQASIABEgAkTAyQnInFw/Uo8IEAEiQASIABEgAkSACPAEyPGlE4EIEAEiQASIABEgAkTgoSBAju9DYWZSkggQASJABIgAESACRIAcXzoHiAARIAJEgAgQASJABB4KAuT4PhRmJiWJABEgAkSACBABIkAEyPGlc4AIEAEiQASIABEgAkTgoSDQTq+lt4enfpM+iQARIAJEgAgQASJABIiAQxMoKS8zk9/g+LKdzPkVq2R2FBUQAYkQcLZzlvSRyIllQQyyjwUwEikm+0jEEBbEIPtYACORYme0jxhaCnUQo0JlRIAIEAEiQASIABEgAk5HgBxfpzMpKUQEiAARIAJEgAgQASIgRoAcXzEqVEYEiAARIAJEgAgQASLgdATI8XU6k5JCRIAIEAEiQASIABEgAmIEyPEVo0JlRIAIEAEiQASIABEgAk5HgBxfpzMpKUQEiAARIAJEgAgQASIgRoAcXzEqVEYEiAARIAJEgAgQASLgdATI8XU6k5JCRIAIEAEiQASIABEgAmIEyPEVo0JlRIAIEAEiQASIABEgAk5HgBxfpzMpKUQEiAARIAJEgAgQASIgRoAcXzEqVEYEiAARIAJEgAgQASLgdATI8XU6k5JCRIAIEAEiQASIABEgAmIEyPEVo0JlRIAIEAEiQASIABEgAk5HgBxfpzMpKUQEiAARIAJEgAgQASIgRoAcXzEqVEYEiAARIAJEgAgQASLgdATI8XU6k5JCRIAIEAEiQASIABEgAmIEyPEVo0JlRIAIEAEiQASIABEgAk5HwIEc3zqoshfD28NT5H8o5sfvRV5xjcBAgvqR2VAJ9tjerEFx3l4kLNoKZZ3t2pKtUXsaCSF94B2aimKNPVLeQ3FqOLw9piJBWW3PAU5RR6M6jfRVofx51S9yK86o7jdAr/tQKb9AVvw89PPwRL9VeRCehQ1oqPmq1hYjL3s3EiJDEZt32452Nagt/goJkUN111YoYneehsquc8aO5ptSpbYYh3VsvT36YMKqXVA6un2awkOSx95G3qpRgvtyH0xOLYTN06cmD7H+wvt5ONKK70lGQ41Kif2Z8ZjPZPRfjbwaSxpJ9frRoCZvNX9fMv/dtIO1JO1Tg+JDm7U2Yb6A/zwkHCpGrd1nTVvfr5lv8Rn/ezHI0m+FRgXlzlWYoNNv82mV7WuJ17+R16Hd7MQq2tLHxF4hq5CutEOfJt/3xWStL3Mgx7deaPMtFQ4nLkdk6AqkFTbd7ahTbseMiOXYcvwX864cpuQeivclYsuVrpgRMxE+dlm6A3ymRGKGXIkta7PtdJYdBoi4oLWnkTTnbygJ/heKygtxMPwOVs/5AMpaSz9ygmY0KpxJWohx4Rm41vMlZFwsxYV3guAqqNLqm5pCpM1ei105CdiSa9/Di6byIFIOABMSTqCkvBDH94bg1vsRmJt4ugE/KC2gqaYC+z/KAyZuxIXyMhR9nYzxqs2Y7sj2aQFMbd2kpvI49mRWCMQIRNjwnrB+y7mPysM5yFELDusfjGFeHQQFbbV5H6rTW/HqmIX49NqTmJlzHiWX1yLIVVwjyV4/+BHK3DwIERuI2mQtRfvcR2X2akxddBnDs86jhN0TDr+A6r+/hnX2POC3+f2aDSytwPvpu7A6MRfiwyvVUCbGILZkNLZf1ep3560YJNkxENW469BwRjRiw5Y+91H52S58gfHYdLkMJVdP4d8ht7B+ykLr+jT1vm+PJpzgz6unh+Cb1DZ/425mLeKYjF5zs7ibAvEe3PyW27lyknbfpBSu6IFgZyM2f8vfxA1k/QzYxOX/1ogGpHDIT0e4VX4enJffW9yRnxoC5AfuyMqRnFfPkdyqIz9IQROrMjTtnP2FK0p5kQtYeYT7ydAL0z+YC0v5jrNOrYrL3zSFC5j7L+70zV8NRzd1o2n61Pf+oCiFC7PLhr9wpUe/5m4YKavl0vBzp75//VZT9HlQepI7esOYrf16Sds+ej5t/dkU+2hlZ5wjG36vuPstFz/p7Qbem2zTaro+D7i7+Uncs36RXNK3N23cA5g80r1+uJ+OcvFrc7mbRtf2A+6nI29z02zd36RonwffcamT/E3u12L3cLHzREL3A1E9tDLz9zej32xmr7e4AJt+TSOvQxNUjbp+LOnz4Cp39Oh142vIUl2BHE277wsa4jjeJzQu0X4Tf4S1x2OWUB2Z+2CEv7kKr/vJgfMp2HGMvd4VC3Vgr6TykKZ7ra19/ROK2NQ8FPMjfNpjnp6SBH6srCoJ0709MSheCW3Eg8mwPXu1HRmPHMPQvbDP3VAqs+tfH/vPg9krC/ZKI1v3Ko0P4WAhG1/pZNEDZq8SUhHLQhb4OkJ59XVMPzWoUR7RjqYMC8TTFkYqTI/Sfu+Epwf1B1CBnNyLbf/aXlzI5inVXMPJrMvw8n4cLoYWO0MRPAylWadQanHQV4Na5U7EbuuBuLdfxiD39oajHW+jA3qN/G90N7oTtEc3Dy/I21gZWa+hGNndmK2smwf62hTMmezTxkaw1X3NOWRty8Un6xKQln3M5N5l6WANas7sx0fn/40N61ORk9eQV9WW2mym8tp8JK/ch57vxWLhYHcbo9asT+lePxr1k5i0ZDTchde2phhZ8Vcx0eqIvETtI+uCngFdoc4vQInhjVwtbpT8gtDgvlbetDnK/eAeSk/kosDHE0+46I0mg6tiNEKLc3Gy1EoYUKOuw2a6Ziw1I/PEyJFPGl9DOhtaOoSVN/6+b61V4316usaljvjNxQ8jx/UEcBsXy++Ix8Swm9rihYhLvyDQ8AI+WbMQ0dvybbzW1b1mmbsJhwXvjtS5SVgavg6fVZq8uMh9E9OnxGBLri66WJ2LxOfewE5DDBt7pbEQ06OTBO2xkI35mLrsU1TyTpeuz4i1+OSKvlMm7xxMjd6FQsPFL1CH39S/4pIjYIQfHjPs1sY35aSuwuQF2YY+VHnvYoKHPi6vHR7ro0AAAHXmESgtxrUZGnXYDU3pKWSf74i+Hl2ML06m0XkrNxpNMTLWpgBTAqDZvVAbQ9fgWDPpY2s/KhC9DTdgCcn7iAKDelsJKHFk+whj20JiEMvirgPjJTrX4B6KM5PxCbs1XfkYcdGzEfLcWuQU2wg3452vfVBDjcL0OCyNCMPzq7LtdJpb8jzUhYfhj/hvTQZe5eOPxQYj7JOhra8fmXsv9DK5ftk9b3/3UPzJWkiJZO3TGYOmTIPvlU2I4H//7kGVtxOHHnsDC0d2tWwUR7kf8AMxZyEP8EA3M8/sLLJPXBP3a9DI69AysRbe0wkjBvUSDDbZ2Z2t+76dzbBqZngbcKxEq6pxvepn0ROkrug40pkDKZ+F5AulKCkvxbnMJfBlN+DERGQU18E9LAnfZS5GJ6ad22LsKSnDmRgF2mnK8FXKQaihwOuZZ7XxRSfjMY6NPqkLUWY24aYfZiR8gXMsDklfD5dx4pJ2spGmOBtxiUoA/RCeegJFuhjGcD851Afi8S82al1zEv/6azbU8vGI/VIb01RycT9ig92hzt2G9DM/ittAcwfXClg/XQVOHRuNfgMjpizA0jUfo+DATuw59yNqlR9gbkQyCgUtGUbV1KW4dsvEoRfUc+xNDWpvlKEUT8H7ifrxXnt00jrMT0HhG4ChUdtwofw8Pl/eDh/NfRPJdsRi2dNH29ZhD06VCJ8XZDIS3LZSAexNxn9wcdZMjDUZCRZK5qj20agOYc1zz2PjnQnIuFgM5QpX5OSqIJ8QCO92Qg2lst0BPhHp2rjwzH8gNrwfcGUHli5Osx4jL/PF7JxLfMzfns2xmOEHFKavtGPwoYX11r0B8h3oj4BhC/Hh5VKc+3IhsC26gbJJ9fphI4pKPP38COvXtVTtAxlcFK9g+94VGHIyFhP6DsSC8mexdvFQ41Ftk9PEYe4HtTdRUgyTN5Amyoh+beR1KNpWCxfWXMShgmBEBpuMBFvt1r77vtUmTHY6oeNroqHgq8zdE3/gHdUdiBzyChIyP8WhCh/EfV2IkvJ0zPaxMrHCcDP4B0beyENO9kdYPXclDvIDsT/jTo3Ja4j+kzFrki//VCPrPgjPDHMTSFKH7y8pUcBKgufg1aDu/BOIzH0s1hy4hJLyo4gL6oq6krM4wNpXf4G4Z/prQx36TkQcP4psJRRB8zOqKtiBj6KLq16ndrxTX3JxjzYkBEp8tDkOW08N4oPoS8ovISvCV/skJHdFl0eYcD+i6q4jp7UQIG+2TZ3DLB+AsaEDdTdcV/jOisbS/t85waRA9lpwN3Z1mY9IBf/412zkmtxQbT4+Su+M2HkDrYwWOKh9NBX4bO0qZHq8hW1vh8HHpR1cnw7EEMgb8UPYZNINbKA93BXPYvY7e3E8NRK+V/Yhy9JDubBlmTsUf34ZcZ9/heTZ3ijcth9n2vINE+94dIQieBwUfPiSDC6+07BseaBuYMTkHi/UxbAt4euHOfaf/R5jFZ0N0lrdkJp9eGHbwaXTE/Cft5B/YCpYsxxv51WKDnRpdXPQ+4FVw1ja2cjr0FJzzV5eDeX2z9Fl9UtQmLyJsNqVXfd9qy2Y7XRCx1eOp9weFR3KlnV/Fm+lv4sZLBZYnYstS2KwNHoBpg8JxASbr9pqUJi6AP16DcX0Rey4OEH4gdDB1DH+fSd0NNDthKf6uAvg30NlWYngu9hmHW5XlGljjcV2M39YVS0+Y/d2BS5XWTjIZSBeXjGNj99Un+uBMa9Yf1q20IoTFMvg8oQnvHAdJTfsT4YD3Met8lJz7rKeGDY5ECguww2LISgOgK02HymZblhq1blsCz2qofzoINyW2bppOqJ97qPy03jEHvDC0iXjDaNxdZVlUMKeDAltYQ+xPtvDPegVLAtHw+YHyLojaGkMZiAPh5QW3mKJddfMZZpb5bjID2QIG+4Ar+HBCLD3PiHZ6wfgwxz8/ghFg+Z8sPfC0rAPe+NTW7gLy5MeYHrUG7oHJiA9YpGVLAEOdD9weRzePkBpyU0bYZfC81Nsu5HXoVhTzVbGHgj3IsstooEDKvbe9xsmqME1a9hhEqytuYGCvGsmr/dN5WRPRDMRx0ZVLx5EckI8Nm5ajDFyFmu2Esv3FVt8ctQUZ+LNNV9AjX6YsWYjEjJPoagkA68LB3JNu7P4vQO6e3pr9/5Qjbuik6hkkHdy004w0oVcsPQtRv/JYRC604buuvaAv0W5dMHybOS7Kh8FZfaMYhhadqoNmddQhPU3njxlcGwtpvvRTfyyFAZiNDHBwXDxaWTKMe7NF+DbkCfyFleTpcXZi8vPLMJsXyuxvbwcDmgfXRgVwiMx2fDWqRoXjh5HtdwLPbuZnqMtDrwJHbjgCe9eDR+l5n/0ezU47KgJgpodqg3xsjRHxI6QKMleP0xVXZiD1UlgZkjqCyRgH7BY3eWbcHOgn/ZNG3PI16ZhTxSsvGlzoPuBfvCknjq/pX0ga+gDcCOvQ5O+m+srn/Lv0jCsiOhj5W2daW8Nue+bHmv9u3M4vmxCSOLfsfG8Gug/B7NEA93ZRLEY7USkkHeRV9sTQWFhCA2bigmjRN1HATl9PCgAeS8MGjcRExWd8f3xA/jK0siq4GjzzfoJZDifhY+P6V7V1F5CGr+IAJtoVgwXNpuTd1D3YGv6Jf4pkI8D5DM8jLK8OIHsUbj1YAeKhGDUFiJn+1l0mdIPgIWAeXUN7vzKpO4Mt46SDC40R9qYEv5G081kdIrNEr6FgMlD4SV6degfHErxzaXvBQ9Kto5rjICteIymEnlbvoTL9NB6p7f2EtJTT7VxZo/7UOWlIaPjBMw0OL01KNy5C8dEX4s7oH3MYvt0s9DZHIAGZ2VpxXNGtKta3Cjrg6gpPqJv3UQPYYW1N1E2YLbA8bdYs+V2uPbF2CldUfrNFcHiLbp7v8UHYZ04kr1+9PI1MMzBlLIU7MNfJ/wPk0A6V3gH9rWSgcaR7gfatwteRpPK7Tz/BES0m428Ds3aaXqBRpWHf+zrgOde1Du9bOQ+E2l89i1L7Tf0vm+pHfFy0Z928aoSKs2NwQg+tZdu1Z++4zA/MVc7CWz9FAuLNbRH9+CZeJmFOVxJRuQQX23MbK9RWHpABcjHIWKcpzbWtqMbnmLqGtKZnUOH3oEYwccHZ2PpMHasL0ZEHAT82NCqiINpA5fMJwyxUQoAF5AeMRy9mT76+F2/mYga7wmZqwLhy8dDDhUOr5mIAR6e6D0kkp+gJw+eh/BBFmK1DClDdKMX+hXcWB9/2Ao8vxCLZ09GANQoWM8ciHtQKb8xzKo2vPJzuNEmG9DNdneAz7QovJy/GZv4ODF2sX2ADfmTEDut/odbU5mN1/wFq9m5DsOC94bg+F/fx05+wRSW8H4fdhUYH2fWnSQKdA+AIZvrJyCxh6G3FiBy03v11wV/Pk5HBjo34Am9uRWsQXH2u5gb8R4S9dcIf933x4R99/E4Pyotoo9D2ketc7jYubQDyTlX2VM2AoZ1ROU5O1Y6am709rTH0jF+9kX9Snr8AgGb8Z/RMzHS8Drd3D78imifKQ3OpUZ1CpvXn0XQgmFWUlLZI1BT63TFyNdiMOLoOqzZoR9o+AZp6RV4eXWY7nfFXB9I9vqp52E5zMFcH8nax3UAJs97GgXrE3T3XfbAdAVZ6acxYs4Y3UCFuT5woPsB7xfMK8KGjUf460OjOoJN64oE5x8ATQVyFozChHjdAkN2XYf150LrbbH0sdlYPWchEjfNwYhe+lUavTDgmUzgcd2kclN9YM99v2laOKbja6azO8ZExWPP4UTrr0JdBiN6bzaS17wIX0MbcviGr0ZyzlqE6maKy7zGY+WSYN1TpBzd8AD3hfHB7Fi/F7Em82Nse2VEI3PedoIi6h/Yk8BCLfTC6PRIWYYgfnKFK3wj1iEjdbU2Lpmvxup8iIyEmfUjc/rDDZ8sF20Q5FBr44U0P+PONTXgNwsbdXrKfKbgb2vGQ67ehw3rM1HZPRA+vCNRP7otnzK64fFgBhkcZMNlMBanvIEu6VPR2yMQc3M9EZfyio3g+/boHrYWGZv9cWIym3QYiLk5rnj1A1vHtQYT7bKVvf+0FgWowCcRg60vWc1uOssisNQoxZ9ezoa+XtMf1xyf7AdsNaZG7zDKOKJtWW5lRJ7VkLJ9RNjoHnBxIAYj+y7Ev2uGI3LBKDzBHkz3fo0a984NGz0V6aJlili+139hOj+IMBTzE/+D2pCliNVN1rXcZxXO/PMl7Q+h/zwknfwN49+M0t3zLB/VGntk3Sdhfc7b8D8eqR1omPM53F57H4stTfSU7PUjpMXCHEowfMoAOx8spGof3W/mX7pgj36y9x8SUDUjEevDeli5RqRyP9AtId1rPOLOq6FOnwOFh+nS0UzHeKzt8m+M6+WJ3nOOwPvdeMvnH2/mxl6HwnOkMdvW9dFUforloTGCuVCCPiy+QWnKfV/Qvo3N37F1LPR12AIJLIaU/pyAAFtnfcgcfIJZSP56tcXlNs01ZY7TVESmAzNSM/jsEuZ1pFPibOcs6SOdc0tMErKPGBXplJF9pGMLMUnIPmJUpFP2sNjHSUZ8pXPiSEYS/rWQAlA3cKY0y7OXWWElVloyGpIgRIAIEAEiQASIABFoEAFyfBuEy5Eqd4Ji7iLMkFvJ92umzn1UHs5BjroHZsRMtBArbXYQFRABIkAEiAARIAJEwCEIOPGUfYfg37JCugYh7nIZ4uzuhcVCxeNCmN0HUEUiQASIABEgAkSACDgMARrxdRhTkaBEgAgQASJABIgAESACTSFAjm9T6NGxRIAIEAEiQASIABEgAg5DgBxfhzEVCUoEiAARIAJEgAgQASLQFALk+DaFHh1LBIgAESACRIAIEAEi4DAEyPF1GFORoESACBABIkAEiAARIAJNIUCOb1Po0bFEgAgQASJABIgAESACDkOAHF+HMRUJSgSIABEgAkSACBABItAUAuT4NoUeHUsEiAARIAJEgAgQASLgMATI8XUYU5GgRIAIEAEiQASIABEgAk0hQI5vU+jRsUSACBABIkAEiAARIAIOQ4AcX4cxFQlKBIgAESACRIAIEAEi0BQC5Pg2hR4dSwSIABEgAkSACBABIuAwBMjxdRhTkaBEgAgQASJABIgAESACTSHwO47jONaAt4dnU9qhY4kAESACRIAIEAEiQASIgGQIlJSXmcnSTl/CdjLnV6ySvg59EgGpEXC2c5b0kdoZZiwP2ceYh9S+kX2kZhFjecg+xjyk9s0Z7SPGmEIdxKhQGREgAkSACBABIkAEiIDTESDH1+lMSgoRASJABIgAESACRIAIiBEgx1eMCpURASJABIgAESACRIAIOB0BcnydzqSkEBEgAkSACBABIkAEiIAYAXJ8xahQGREgAkSACBABIkAEiIDTESDH1+lMSgoRASJABIgAESACRIAIiBFoJce3BsV5e5EQOZRPmcZSZnj7z0NC5jEU12rE5HLwMp2+i7ZCWddcqmhQW3wMWfGrsFlZq2u0DqrsxVqmkdlQNVdXzdoOk/srge37YHJqIZzR6s2KjRojAkSACBABIkAEmp1Ayzu+mkrkrX4JIRHLsSVX4Jqpc7FlyWyEPPc+8lT3m12xtmywTrkdM5i+x39pPjHqziF5+mwsS1TiQfO12got/Ygzae8IbK/G9aqfyfFtBfLUBREgAkSACBABImBMoIUd33so3rEckWkXAHkwovaeQlF5GUrKz+PA9iUYIwdwJRmLt5xEjbFc9M0uAu3gHpbELzpSkhwGd7uOae1K9/CT6i4AOQLWfMHb/0yMAoaVU1pbHOqPCBABIkAEiAAReGgJtKzjW/M1dqw/AUCB19M3YNFgd2g7dIXP2HlYtvx5zFjzD6S+PgyuBhOYhkX0wYRVqcgrFrrG/4OcSAW8PRSYn/kNlNnxmO/vyb/y7xe5FWdMRpA1KiVy4uehHwux0IdZHCqGPmCA77q2GHmpqzBBXydkFdLyhHXs6VMbevD0lCRUs0arkjDd2xOD4pWog/74Z/H37EysCekDbw/9a3/TcABdKEi2EioWE6DKxnzvqdhSxRq9gi1TAuAdGA9lnaVQB31YhEBnM32Ex+6GUpldH47gPw+bT6tsj8oyZpn17L09QhGbmlcfvsLk9vgjluYywdUoWDMevT0WI0fVbPEfhrOGNogAESACRIAIEAEiYItAiw681ZWcxQE1ALcRGNmvk4ksHeAT8TfEGZXWoDB1BZ5b8wXYYdo/NQrT1yIy/TO8nrkd0QphO1U4vOQFHNZXZe5V7jq88EMHHMiKgA/zsmtPI2lOBLZcqW8RLMxi7kUUJezGlrAekGkqkLNsFpYeEIRiXPkYcRGHcGJNMjZF9IGLoQ9rfYajo6GepY0r2Bq9VLezB/p6dAEqP8Xy0BgcFIjIyxh9EUXYjS1DLLUlVq5BbeEuLJkci8PC9nh9srAnKhW7YwYL9AGQ+yam5wraUuci8blf4PpVMmb7dBDsEGzWXkJadCTihOEruIBP1szBJ7uXYM/ehVAIqtMmESACRIAIEAEiQATamkALjvjW4XZFmXbkc6AnutvhYmuKM/Em7/S6Y8ya/TjHwiKunkDy7H4AlNiycieUppPh/GZh41fnUVJeiGMJYWDREzivxOXv2ajiPRTvS9Q6vX6RSP66kK93PDUSvlDh4F+341hNHWqObUfsARXkwXH4/GIpSspLce7LOIyRq3B4/R6cqTGZimWxT/ChB99lLgbvnrstxp6SMpi92vdbgj2sn6sHsOIPcpQe3IeDajl8o/bodD6KjSEscEGFb8tuQ+Mehg9LMvC6G1POD69nFqDkbAwUYkw1xchY/j7v9NbrUwitzmoUJv4NyUp+PFpw7vXDjIQv+L6LTsZjHA/xMk5cui2oI9xkXN/XOr3y8Yj9kvEvQ9HXyQj3kwNXtiJ2Wz5qmdzl/8HGYCa4G8Yk/Acl5UkIdRcTXNg+bRMBIkAEiAARIAJEoPkJtKDjKxD2h2rcNfEdBXt1m/dQeiIXBexb/1ewbJZulFXWHUFLYzCDjwc+gGNFwmFMOQKen4k/+7BAifboPmQUjAdHb+Py8ctap+uV2Qhyb8/Xcw9aic+ZU315LYJc76Hk7Gl+hFmdG4sJfb3g7eGFAc/oRkzVeTik/FEgrq0+BVVFN9nx4zDARQbI5HCRy+ETkY6S8rPYPuoODmVnIu2tRYbR5/t3agSj36INGhVqSk8h+zxjNBxLV0yDL+sH7eEe9AqWhffgHyDSj16FUbBB/8mYNcmXHwWWdR+EZ4bxHrZRu0ZfNNdwMuusNm53eTRe8tUGqsjcR2PJimmQQ43CHcdRZNSJUQv0hQgQASJABIgAESACrU6gBYfe2qFrD09+5LO6okrr+Fp1s+twt0rrYHYK6gdPYV25K7o8wuIYVLhcUc1ChnV/j+D3nR7VxQ0D6NoD/m7AYT4WFkDd9yjLZ1+sOXLVuH5JEOKgb9rweRe3qu8ZvgE2+hTUFN/syoc31KtnITRBd3D7Lq7aUWzxxsxKNXercJ2Vug1EgKcwTKEDXLs8ytevvlSB22Cj6Lq/33dCR4NAnfBUH3fAKIRBX1H3qfkZVRXMufbDqH5P1POHDHLXTmCPF+qqMly/XQeFNGfcmShEX4kAESACRIAIEIGHgYDB3WkJZdt5ByKEjdRWHcexC6av1zWoyVuH1+L36iautUNHt868GNV5F1AmHCFW1+DOr2yXO/x7CGN8bUjd7jF4DmRO76/4odpSCq0O+H/u2sjcTlEZ+I7POsEyT+j/lfgw7EkbHTVk96Po4jJs1CkAABgxSURBVCpwSA2hCXL4hsdi4+YMHL9agD1Rfg1p1FBX1tENT7FvVfkoKBM67PdQc+dnvl6nPj3Q1XBEIzZkj8KtBzPsNRy9cEMwCU4DdU01+OR0bp54qmsLPlc1Qmw6hAgQASJABIgAEXi4CbSo4wvXAZg8jw3PKrElfJkgU8B9qE5/iDde24qDicsR+UYmijUd4DU8GAHMHuc/wIYdl7RZF1ge4I3x+IQfYAzByN58AKqdVusK/xH+2owCu/fhGJ/tgY2wpuuyQIQjrVgORXAQP6pavW0bPi5k2SPuQ5X3rjbDg/9q5JnG+NrZu13Vam+ipJgp54qeg4Lx5z8r8Nj33+DTg9fsOty0ksxrKML6M0YnsHHdPhTyMdFMnw+wIb2Cz7ARPqpX09KJyXpi2ORALdf1CdjJMwM0qiPYtG4f1JDDd9YI9Ca/19Q89J0IEAEiQASanYAgSxHLzCTZBZ2aXXFqsBEEWtbxRScoojZrJ6fxmQKGojefLswXI55bp806wCZHrZ/CZ2CQ+YQhNoo5yiocXjMRA1jdXsO1eYBZSrR3X4KCj1m1V9MO8JkWhdf5CVfJiBziK4jflcN39hw84yWH66DpWBrsDqi/QNwz/eHt4YsREckohDvGLJ+OQa4Nw1Q/6ipMZ2ZBZpdeGDRKO5HtYPQonk/vIYtxCt15Z9wQ42sYZRWmMxNpU+aDqatfhS9zSw0xy3p92AS6NxFplBlDpA2bRQKuBmae6D0kEukse4bfq4ibN9A4c4TNNlu7gjblWw5LxxZo4eGmthiHDWnwWFq9XVCapMoDalB8aLMhnR6/IqFpqrzWUo2ll8vejYTIUMTmiU1MtENnJmtNHmJ16QH59H8e7AFR+PagNRSyR9b7UCl3IZZPDTgU85NOadP/GYnHHrK36uzDbJhdn27PqF5rf2H6CVc0HIr58V+ZyaZRnUb6qlDLaRhbW2wr/dmW1eRaCVmFdKUdaROt9Nlyu+yzDzQqKHfq0mDamway5YS20DJ7u7q6Pp2nPmUn/ym8th3JPqaq6nLaX0jBDLkcASP88JhpFQf5ztKv7tenCTUbeBOxZWgqioVvyCWmp2V92u58a5hH1xigbHLa2p04kLoerzPn0vDXj8/hu+dwImbrJkeBOcoxKSZ1WQjAaiR/lWKSyszQkPUNl8FYnLITG6OC62Nl5cF4PWEntq8eC3dGwKUPZifsQPKaF3mHkW+Q1dm+wySVmfWu9HtlXuOxcom+Pzm64QEsug2yHvjz6iSsCdfH3PbDjLhUpG1fyE/UU2cegZKNOMs88cyqRdpFP1hHLDPCPbGzXQYXxULs/ioNG4Q6+72I2NRs81RmeqEb+ukyGNF7s5G8aXG9TGA2TcEBlsqsQQ8oDe286fU1xTsw572dyFmVhMN8GI1Jm5oK7P8oD5i4ERd0GSvGqzZj+pwPBJlF7qMyezWmLrqM4Vm6zBaHX0D131/DOlHH06SP5vyqKUTa7LXYlZOALbmmYUXajmzqzFe7j8rDOchhLyH0f/2DMcxLEJ6jL2/BT9uyalCr/ABzV5ZhbMpZlFzNwMw7f8fcxNOC/Nwa1J77ErkIw9bL2qwj41XrMPVvx9p8wRwNn8LwLVwekazL5JKBmdVbjGVjqRhf+QhVoR+giGWayRqFy4tmYXl2hSC8qAWN0JCmbcp6H5Wf7cIXGI9Nl1m2nlP4d8gtrJ+yEElmWWYa0nHL1LXLPqiGMjEGsSWjsf1qGYoOv4A7b8VIUJ8foczNE58kbbi2Hcs+4lbXoEZ5BDnqQIQN7ymYeyJeW3ql2of0V8csxKfXnsTMnPO6CfgCN03zPziy+6DAlnIETB4KL0EV6ehlTZ82Pt84wZ9XTw/BN9okAtIn0LRz9heuKOVFzsvvLe7ITw+MlH1QepI7euNX47KiFC6s50hu1ZEftOUPvuNSJ/lzASuPcD8ZamrbNC4z7LS50TR9OO6BqYxmPVrWma9691suftLbZjzMmrGzoGn6WJGVZx9cbwsmz09HuFV+L3KpRb9opXtwlTt69DpXb9kH3E9H3uICROxtpzpc0/TR9yKuF287g2xi59Gv3I2s6CbJr5dA/9mc+hif8yaymtmC4zjR60cvWeM+m1Mf0/uCsX1015rBXkxe3fk1KYUrqj/pGqeI7qhm0eeno1z82lzuppFMTNa3uWkp32mvD4eyjyWkP3BHVo7kvAZs4vJ/s1SnecubxT68SA+4u/lJ3LN+kVzStzcF9yyhvNo6YUa/N8L9Td9uNX3a+HyT5HOCdJ5YSJKHlYCs11CM7M7yU9T/ybp5oK8wxFzWBT0DukKdX4ASQ37pWtwo+QWhwX0FqxHWtyHtLQ1qzuzHR+f/jQ3rU5FjtHKhtCTXpu3rBu8n6peWgWtfjJ1yC9knrmlHRGWeGDnyScHIz33cKq/AU/MmNjh8qXm1b49uHl6Qqy/iXIl+RUoNam+U4fqU0VCw0Co+ZeBleHk/LggZag/3Pv3hZZZisXmla3Br9shqZgsAuuunwf21+AF22Ae69Js+nnjC8HZLBlfFaIQW5+JkqcV3fC0uvWkHGvWTmLRktPbtpn6nphhZ8VcxUT8y6lD20Sth8llXgXOfV0A+IRDejja/pDYfySv3oed7sVhoWOHWRD/8iDOZ+1CQHo8Nqdkmq9ma1m3j77b0aePzjRzfNj4/qHsHI/CIAoN66xfY7oxBU6bB98omRETvQmHtPajyduLQY29g4cgm5c1oGyj8jyGbnMhWS4zD0ogwPC+ZmFghEp3TIfdCz27GDydsYmpB1imUmkYB8UuSv48NZeHYHmWycqGw6VbZlsF10ES87PcdtoT/BWmFNfzE0MTcJ7FVv3w7P+nVPAZH+/B1GxfL70gn3KFJsnbCiEG9BM59qxjARid22EeXy1we4IFuZr+iZ+sfvmz01Bq7Ze690MvgnGt7ZA+O+7uH4k82Q5ikaB9xapqyCzha1QMTvO/iU31cvEcoYrMLBeFP4se2baluoS38Ef+tycCr/PwK85h/TfF+JPIT1NkKqTGI/NNLEtXNPn3EmbfO+WZ2yYoLQ6VE4GEnwOLH/oOLs2ZirGEkmMVTv4Lte1dgyEm2+MlALCh/FmsXDzUeXXEUdDJfzM65xMdf7tkcixl+QGH6SkSzVfgkpQMbVb8OGI22WRJQNxmk7zhErtmBw98ewzel+lFWS8e0Qjk/9yAZUcPO8RNqe79yHS+8PQ+D+EV22LyDx+HtA3EnHqa5wFtBXmtdNFbWmos4VBCMyGDhqLy1jlpxny378M4+TEbkW1G+JnXFHhyVePr5EehuzQOQsn3M9K/D95eUKEAFPj9+A0+/vhclF/cjNvh7fBIdh4xWn5xrJqDlAt0bE9+B/ggYthAfXmYrxy4EtkUb3XtlPhHI4uebZCCBn490AZ9E/1VkJVbLXbXKHjv1MZOlFc83a6e9mVxUQAQeWgK1+fgovTNizbJVtINLpyfgP28h7ygWrFmOt/MqpTMa1xiDydyh+PPLiPv8KyTP9kbhtv3my3Y3pt02OUYG16C1uFBeiOOZ72IG9mFp6GrkVPLZpttEIn2nMpfO6NFnOl5nE1vPb0D02kP1WSlkPpgcMw1yo9SOKihzcqFUP2Uc4qFvsK0+GyVrNZTbP0eX1Q3N1NN6Slq1T+uJ0fw9Mcfks99jrEKbN1+8A+nbx1juanx35jzgtwSpCfO1D5Auvnhm4mAAP6LqroSXEeUfojpCETwOCv7BVwYX32lYtjwQhYmJZk67zF2BiRHv4LOvkxHu9x0+yjzX5pN1jWzRQH20x7bu+UaOr5HF6AsRECNQDeVHB+G2zPRHWrvq3vKkB5ge9YbOUQTSIxZJcGa3mF42yvTLhcN02W4bx7X4bhc84f0UUFyGG4bYaludtoe7YibWJi1DgFqJM0VtPOpbewlpy3YCzy9E9Dt7cTx1JpC2WJCVgjnsS5GxfSawnqV2HIr5iYdRUFiAQsNMfFs6t9b+hsrKMnLsRZZbRDOkVmwhHW3ZRzfKXVpyU2JvQ2zz4MMc/P6ojSUXre4A9jGVm40WZt5GwPPjMMAQ1lGHu9VsNVhveHZv3aw0puJZ+665VY6Lwiw6fGX9ugbXUXJD/H2bzH00lqyYBugzP1nrpBX3NVyf1j/fyPFtxROCunJEAiztyl5cfmaRIO2eTg9+1b1NuDnQTxvawKfuS8OeKGDL2mxJ51a02xL8D3wvaY0wQv+jYKKF5g6uFdy1mt5Hu8CLaVywSTst/pXFwL2PuEpv+PMjPO3hHvQX7M58FTAa4XGFz9hF+JCl/yo/hQ+jBgIFasyImcjnPW9xMRvUgf2yaioPIuXSMKyI6COx2F69wnbYx7CIj/4Y7af2R1/K6bR0YQ5WJt9K3z7GzNk3LXeTECB9HHbIGAx+TLqz3azH7Vt7uyODyxOe8LIr5MucWUuVNFSftjjfyPFtKetTu05AgK14l4aMjhMw05BrugaFO3fhGMutLDqpxxXegX3rc0Y7OoXamygbMBuTfaQ1YsI7sD4ncUjJRnR0f7w9/K3n8GR1KvoKJijqD27NT12MslGXMrh4B0AhzBoi3M9WsFz7V+wJeg8rgiQ+cdKKrBpVHv6xrwOee1Hv9LK3JplIOya24IoQQGtu22Mf7cOXl9FomzYzR6nkRuQF7GyEOTiGfQT68Jv6ya5BgvCN+6j8dCs2Fo/E0ugx1mOZTZtr7e98NpquKP3mSn2oE+w5l1id2+gvtQfhBujTVuebkzu+tVDGP6td9chotRpPeLNXh/HZgpW4TJY89FiMHJUwLsh0xZRnkaA0fQXBVpLKRkLkmybH6q4k4Upg/vOQYPcKX9VQxk+FdwNX0NIUp2KyRx9MiBcm9W/tq9pR+6tBcfa7mBvxHhIjhutWHGTnTX9M2Hcfj7PXafyS3E+jQLBsM2qvICv9NEbMGSPRpOKW7cGvsPOZ0nDz1ahOYfP6swhaMEx6qdn4FQonQbnuA+Sx1fT4pc03QzkvClN1TrqmMhuv+YcidudprU58nWTciooUTFC0zKPl9uiygQjjd1GDwszdODBqmslM+xoU5+1FwvxI7OryhgQyUlijYk1WthJaNlbPWYjETXMwohe7lti/FwY8kwk8LkhLZ62LVtlnn334lUbnFWHDxiP8+aVdsr0IL68Ok+CIvBac5TAHR7KP6UlwG5ePX4bckAqQrab3NuZFX8WUf8biJcOghelxUvneFSNfi8GIo+uwZsclPnRGo/oGaekVgnOJ+RZfYL9hpUO2OMR2bDgWiFcll0HIHn3a+HwTpjxuvuTFwlbbcvsul78phE86z3QT/R+fxOXfZZm9f+NuZi0S1BEsVMCrYNpWCBeff1en3E9c0ZEUbtV4f93xi7jsmyYZtB9c47JfHcJ58cnNdcmqew7hFmRds5Csup6bdlECD5OFEur3W97SJfTuKUjqb7myQ+5p9DnLL3YgPCf8uTB9MndOl3xf9JwR1mM5629y+TtWcs/q6/pFcvG5RZz+zGgo1Ebrw+ltLdDJNJG+VZ2ZKrncav05zPTIOMoV8ddGQ7Wor99ofWzIqu3hV+7mt//i5vkxnSdxq3Z8a5yk/+5FLnXuEMM1HTB3E5edbyk5fL3M1rYarY9Zo79yN/M/FtwzhnDzNh0U8Nbb0597dmUKd6SofokUs6aaUNA8+tiW9cGNLG4BbyfB+am/ZkzP0zbXhwlgyz46IR/c5E4nRnIBTJfxK7mdTTy/TFVvHvvoW2WLoqzk4vOr9AWGT8ezj0F0na2yuHjDtd6y14yw5+azzwPubtHBeh3MzqVfuZtH3jH8zrB7WeaRxv/OCHUQbreWPm19vqFllBa22pbbemc1kJuXdV0giPAHU+/gmjq+Jo6mbpUhdmJo/+sd39/yk7hpK1bofoDZflPHV7eiT08PbuCmfI53iX/L5+IHeIiuGiYQlOMMDo1eTuO91r/V92u8qpL1oxxpb/NdqNLQmvSRhh0sSUH2sURGGuVkH2nYwZIUZB9LZKRR/rDYx8lDHSy9ymgP98ETMWGYG4C7uFVtssrO6Ocxo78cakH8lnalKDXkz72I59hhgr92ikXY+7f38Pd/zrIQ26lfK12Op9weFawkBUB9GudKzKZ01rfOz1atANAfg57uVF9u15YMrk8HYgjrRqCLXYdSJSJABIgAESACRIAIOBmBh9TxZfEx+/H5ySoA7vDvYeJQ/p9+GDs5UOCU6oLn0QOh44ahm+hJIIPctRNE54vzs83Z5I1H8PtOJo4vVLhcUS3aIsAWTTiCHOYX91fA32xmKoupy0baqnC8ll3B547VxjUK4nof88Pw/nJAasucWtCYiokAESACRIAIEAEi0FIEpJvjo1k1rsLh6D/CO9q8UXnIfEwfwCZWCCeyyeHdbyA6IRlHL9zAYkUX7UpRbNTVrwvKzJuxXqL5GVUVzHt9RKReFZRl36MOT8LcGPdxq7wU7EjzpTHZZLxVCIn+TNumSonvw3rgMVlHPNYTOJh3CTejBsNH1gU9A7oC5/XLnHY1HnEWkYiKiAARIAJEgAgQASLgjAQe0hFfZsp+mLEmBRkbJommOmnnHYgQuVq7ZGg1S45doRt1/b+teB7U4W6VNl1T+y6uJmEU7eAelgBlqi684odq3NUAMvexWPXuq/jD5KG6rAId4NrlURbsgOtVPzv2imKtSJ66IgJEgAgQASJABJyPgPkgo/PpCMANYxI+xYdhT9qvHZ+Lrgc+Sf8SOSnuyFHLdYnxf7a/DX1N2aNw6yEHWGSF2Z8bFJ6PiYz2sorVuH5JZXZEfYE+hncHDldU8Y4vZPdQVvEE3pjmQyO79aBoiwgQASJABIgAESAC5BtZPgc64elB/QF8ja2J2VCjCavx6MMN8Ct+qDYddRWJMTYI1QlP9XE3fLO68Ws1atR1qFXm4GSPMVAYlm20ehTtJAJEgAgQASJABIjAQ0PgIQ51sGXjdnisjwIB+mpyL/TsJjp1TV/DymdnKIKDIBcLN5APxgBvS8s1tUNHt858u/fv1PCxvmaddO0Bf5ZlQl2Fn27lI+OCD6YqhJP17qHmDhulFskoYdYYFRABIkAEiAARIAJEwHkJkONrxbb8sqgsIwJzG/Wrwlisfx/fV1TgPr//R1TfFU6Wk8F15FzEhbijOu8CyjQa1F44ga+q3DHuvbkY6WrJDO3RzcOLj+1VF5TjlsZi5wBK8HlaMQKmDYDRGkiGjBIm65hba4r2EQEiQASIABEgAkTACQlY8ricUNVGqCTriWEsrRlLYxbc1+KyrXXKeAzy8MXIaBYSwf5OIO5PfvAOjIdS7//KeiB0Qyo2BmQhpJcXBoRfwJ+278D6sB5W4k1kcFWMRijzvYvLcKPWmuf7X/CfMtE8xKH2JkqK1YBcuI55I1jQIUSACBABIkAEiAARcHACTj65zQWKmP+Pkhh7rMSyJCShJCxJULkDfCLSURIhKGqnQPTZMggzo7VTxOBMuR2duPgi9J0chL4jaM/WpmGSXR4OKRchKKiryBFy+Ea9iUijEAdWrT4PsDx8NBQWR5ZFmqQiIkAEiAARIAJEgAg4GQEa8ZW8QTtj0JRp8EUFcnIvogYa1Co3Y0LIZihrNdCUXcCJIe9iW9Rg4xAHXi/9inHDsXT2EIsj1pJHQAISASJABIgAESACRKAZCJDj2wwQW7YJGVwUM7AsvIdu2eFaFB09gMIr+5B1phTnTvwX/mIhF7Gm8jj2ZFZAHh6JyT4dWlZMap0IEAEiQASIABEgAhIn4OShDhKnb7d4XRH0zlGU8CESGtSOCoFv4lYocy9h1pvPwcdC6jJZ9zD883KY3b1QRSJABIgAESACRIAIODMBcnwdzrpsBHgRPi9f5HCSk8BEgAgQASJABIgAEWhLAhTq0Jb0qW8iQASIABEgAkSACBCBViNAjm+roaaOiAARIAJEgAgQASJABNqSwO84juOYAN4enm0pB/VNBIgAESACRIAIEAEiQASajUBJeZlZWwbH12wPFRABIkAEiAARIAJEgAgQASciQKEOTmRMUoUIEAEiQASIABEgAkTAMgFyfC2zoT1EgAgQASJABIgAESACTkSAHF8nMiapQgSIABEgAkSACBABImCZADm+ltnQHiJABIgAESACRIAIEAEnIkCOrxMZk1QhAkSACBABIkAEiAARsEyAHF/LbGgPESACRIAIEAEiQASIgBMRIMfXiYxJqhABIkAEiAARIAJEgAhYJkCOr2U2tIcIEAEiQASIABEgAkTAiQj8L6c2gsdgmaPeAAAAAElFTkSuQmCC" alt></p>
<p>Use the scatter diagram to find the value of \(a\) and of \(b\) in the table.</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</p>
<p>i) \({\bar x}\) , the mean distance from the power plant;</p>
<p>ii) \({\bar y}\) , the mean concentration of \({\text{PM}}10\) ;</p>
<p>iii) \(r\) , the Pearson’s product–moment correlation coefficient.</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>Write down the equation of the regression line \(y\) on \(x\) .</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>Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of the regression line to estimate the concentration of \({\text{PM}}10\) in the air at his school.</p>
<p>i) Calculate the value of Ernesto’s estimate.</p>
<p>ii) State whether Ernesto’s estimate is reliable. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A manufacturer claims that fertilizer has an effect on the height of rice plants. He measures the height of fertilized and unfertilized plants. The results are given in the following table.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">A chi-squared test is performed to decide if the manufacturer’s claim is justified</span> <span style="font-size: medium; font-family: times new roman,times;">at the<strong> 1 %</strong> level of significance.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The population of fleas on a dog after <em>t</em> days, is modelled by</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">\[N = 4 \times {(2)^{\frac{t}{4}}},{\text{ }}t \geqslant 0\]</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some values of<em> N</em> are shown in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null and alternative hypotheses for this test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>For the number of fertilized plants with height greater than 75 cm,</span> <span>show that the expected value is 97.5.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(\chi_{calc}^2\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Is the manufacturer’s claim justified? Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i, f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of </span><span><em>p</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii, a, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, a, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the values in the table above, draw the graph of <em>N</em> for 0 ≤ <em>t</em> ≤ 20. Use 1 cm to represent 2 days on the horizontal axis and 1 cm to represent 10 fleas on the vertical axis.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">ii, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Use your graph</strong> to estimate the number of days for the population of fleas to reach 55.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, c.</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>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The heat output in thermal units from burning \(1{\text{ kg}}\) of wood changes according to the wood’s percentage moisture content. The moisture content and heat output of \(10\) blocks of the same type of wood each weighing </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(1{\text{ kg}}\)</span> were measured. These are shown in the table.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the above data. Use a scale of \(2{\text{ cm}}\) to represent \(10\% \) on the <em>x</em>-axis and a scale of \(2{\text{ cm}}\) to represent \(10\) thermal units on the <em>y</em>-axis.</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><span>Write down</span><br><span>(i) the mean percentage moisture content, \(\bar x\) ;</span><br><span>(ii) the mean heat output, \(\bar y\) .</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><span>Plot the point \((\bar x{\text{, }}\bar y)\) on your scatter diagram and label this point M .</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><span>Write down the product-moment correlation coefficient, \(r\) .</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><span>The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . Draw the regression line \(y\) on \(x\) on your scatter diagram.</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><span>The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . Estimate the heat output in thermal units of a \(1{\text{ kg}}\) block of wood that has \(25\% \) moisture content.</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><span>The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . State, with a reason, whether it is appropriate to use the regression line \(y\) on \(x\) to estimate the heat output in part (f).<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In an environmental study of plant diversity around a lake, a biologist collected</span> <span style="font-family: times new roman,times; font-size: medium;">data about the number of different plant species (<em>y</em>) that were growing at different </span><span style="font-family: times new roman,times; font-size: medium;">distances (<em>x</em>) in metres from the lake shore.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the data. Use a scale of 2 cm to represent 10 metres on the <em>x</em>-axis and 2 cm to represent 10 plant species on the<em> y</em>-axis.</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><span>Using your scatter diagram, describe the correlation between the number of different plant species and the distance from the lake shore.</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><span>Use your graphic display calculator to write down</span><span> \(\bar x\), the mean of the distances from the lake shore.</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><span>Use your graphic display calculator to write down \(\bar y\), the mean number of plant species.</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><span>Plot the point (\(\bar x\), \(\bar y\)) on your scatter diagram. <strong>Label this point M.</strong></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><span>Write down the equation of the regression line <em>y</em> on <em>x</em> for the above data.</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><span>Draw the regression line <em>y</em> on <em>x</em> on your scatter diagram.</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><span>Estimate the number of plant species growing 30 metres from the lake shore.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">George leaves a cup of hot coffee to cool and measures its temperature every minute. His results are shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the decrease in the temperature of the coffee</span></p>
<p><span>(i) during the first minute (between <em>t</em> = 0 and <em>t</em> =1) ;</span></p>
<p><span>(ii) during the second minute;</span></p>
<p><span>(iii) during the third minute.</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><span>Assuming the pattern in the answers to part (a) continues, show that \(k = 19\).</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><span>Use the <strong>seven</strong> results in the table to draw a graph that shows how the temperature of the coffee changes during the first six minutes.</span></p>
<p><span>Use a scale of 2 cm to represent 1 minute on the horizontal axis and 1 cm to represent 10 °C on the vertical axis.</span></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><span><span>The function that models the change in temperature of the coffee is <em>y</em> = <em>p</em> (2<sup>−<em>t</em></sup> )+ <em>q</em>.</span></span></p>
<p><span>(i) Use the values <em>t</em> = 0 and <em>y</em> = 94 to form an equation in <em>p</em> and <em>q</em>.</span></p>
<p><span>(ii) Use the values <em>t</em> =1 and <em>y</em> = 54 to form a second equation in <em>p</em> and <em>q</em>.</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><span>Solve the equations found in part (d) to find the value of <em>p</em> and the value of <em>q</em>.</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><span>The graph of this function has a horizontal asymptote.</span></p>
<p><span>Write down the equation of this asymptote.</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><span>George decides to model the change in temperature of the coffee with a linear function using correlation and linear regression.</span></p>
<p><span>Use the <strong>seven</strong> results in the table to write down</span></p>
<p><span>(i) the correlation coefficient;</span></p>
<p><span>(ii) the equation of the regression line <em>y</em> on <em>t</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the equation of the regression line to estimate the temperature of the coffee at <em>t</em> = 3.</span></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><span>Find the percentage error in this estimate of the temperature of the coffee at <em>t</em> = 3.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A biologist is studying the relationship between the number of chirps of the Snowy Tree cricket and the air temperature. He records the chirp rate, \(x\), of a cricket, and the corresponding air temperature, \(T\), in degrees Celsius.</p>
<p class="p1">The following table gives the recorded values.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_08.39.25.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw the scatter diagram for the above data. Use a scale of 2 cm for 20 chirps on the horizontal axis and 2 cm for 4<span class="s1"><strong>°</strong></span>C 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 class="p1">Use your graphic display calculator to write down the Pearson’s product–moment correlation <span class="s1">coefficient, \(r\)</span>, between \(x\) and \(T\).</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 class="p1">Interpret the relationship between \(x\) and \(T\) using your value of \(r\).</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 class="p1">Use your graphic display calculator to write down the equation of the regression line \(T\) on \(x\). Give the equation in the form \(T = ax + b\).</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 class="p1">Calculate the air temperature when the cricket’s chirp rate is \(70\).</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 class="p1">Given that \(\bar x = 70\), draw the regression line \(T\) on \(x\) 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 class="p1">A forest ranger uses her own formula for estimating the air temperature. She counts the number of chirps in 15 seconds, \(z\), multiplies this number by \(0.45\) and then she adds \(10\).</p>
<p class="p1">Write down the formula that the forest ranger uses for estimating the temperature, \(T\).</p>
<p class="p1">Give the equation in the form \(T = mz + n\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A cricket makes 20 chirps in <strong>15</strong> seconds.</p>
<p class="p1">For this chirp rate</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>calculate an estimate for the temperature, \(T\), <strong>using the forest ranger’s formula</strong>;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>determine the actual temperature recorded by the biologist, <strong>using the table above</strong>;</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>calculate the percentage error in the forest ranger’s estimate for the temperature, compared to the actual temperature recorded by the biologist.</p>
<div class="marks">[6]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br>