File "HL-paper3.html"

Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Math AI/Topic 4/HL-paper3html
File size: 682.53 KB
MIME-type: text/html
Charset: utf-8

 
Open Back 
<!DOCTYPE html>
<html>


<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">

</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>

<div class="page-content container">
<div class="row">
<div class="span24">

<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>

<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>HL Paper 3</h2><div class="specification">
<p><em>This question explores methods to determine the area bounded by an unknown curve.</em></p>
<p>The curve&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>&nbsp;is shown in the graph, for&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 4.4">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>4.4</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>&nbsp;passes through the following points.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">It is required to find the area bounded by the curve, the&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis&nbsp;and the line&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4.4">
  <mi>x</mi>
  <mo>=</mo>
  <mn>4.4</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>One possible model for the curve&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>&nbsp;is a cubic function.</p>
</div>

<div class="specification">
<p>A second possible model for the curve&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>&nbsp;is an exponential function,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = p{{\text{e}}^{qx}}">
  <mi>y</mi>
  <mo>=</mo>
  <mi>p</mi>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mi>q</mi>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>, where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p{\text{,}}\,\,q \in \mathbb{R}">
  <mi>p</mi>
  <mrow>
    <mtext>,</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mi>q</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the trapezoidal rule to find an estimate for the area.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>With reference to the shape of the graph, explain whether your answer to part (a)(i) will be an over-estimate or an underestimate of the area.</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>Use all the coordinates in the table to find the equation of the least squares cubic regression curve.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coefficient of determination.</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>Write down an expression for the area enclosed by the cubic function, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4.4">
  <mi>x</mi>
  <mo>=</mo>
  <mn>4.4</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = qx + {\text{ln}}\,p">
  <mrow>
    <mtext>ln</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>y</mi>
  <mo>=</mo>
  <mi>q</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mrow>
    <mtext>ln</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence explain how a straight line graph could be drawn using the coordinates in the table.</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>By finding the equation of a suitable regression line, show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 1.83">
  <mi>p</mi>
  <mo>=</mo>
  <mn>1.83</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 0.986">
  <mi>q</mi>
  <mo>=</mo>
  <mn>0.986</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the area enclosed by the exponential function, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4.4">
  <mi>x</mi>
  <mo>=</mo>
  <mn>4.4</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iv.</div>
</div>
<br><hr><br><div class="specification">
<p><em>In this question you will explore possible models for the spread of an infectious disease</em></p>
<p>An infectious disease has begun spreading in a country. The National Disease Control Centre (NDCC) has compiled the following data after receiving alerts from hospitals.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
  <mi>n</mi>
</math></span> against <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
  <mi>d</mi>
</math></span>&nbsp;is shown below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAV0AAADoCAYAAABM+DfFAAAgAElEQVR4Ae2dCZhV1ZXv/zVSVBUU8zwPxSTIICKDDGIcUFFM1JjE1nQmkzxNXr7ufknMS6ff63TSSSfpTpuXyTglxjgEkCgOCMgsAiKDMs/ILMVMFRRV7/ttsvF4c29RVN3p1F2b73BunWmv9V97//c6aw8nq7q6ulqWDAFDwBAwBJKCQHZScrFMDAFDwBAwBBwCRrpWEAwBQ8AQSCICRrpJBNuyMgQMAUPASNfKgCFgCBgCSUTASDeJYFtWhoAhYAgY6VoZMAQMAUMgiQjk1pTXjh07ajpd53O5ubnKycnRxo0b9cgjj2jLli168MEHNWHCBJ0+ffrCc7Ozz7cJK1as0C9/+Us1a9ZMDz30kNq3b6/33ntP06ZN0+rVq1VZWalGjRqpT58+uuWWWzRw4EB3rKbRcFy/YMECPf3007r77rt1xx13XMg3rD/Q99ixYzp79qxatmyprKyssKri5KYsoE9JSYkKCgpCrQvCY58TJ064stm8efPQ64N9Tp486eoldbohpDNnzjg7wQ+JSklFChKg4G3fvl3Lly93xPn2228Lg3mC8Nd4hQ8fPuyufffddzVixAhBxBxbtGiRe85tt92mkSNHav369Zo1a5bmz5+vNm3aqFWrVi4v/xzbGwKGgCEQC4GKigqtWbVSGzdscBwzeMgQlfbt737Huqeux1NCups3b9aLL76orl276vrrrxeEitLBhCdMK4qX+8EHH6h///7Ky8tTVVWVtm3bpq1bt+qKK67Q2LFj1aFDBxUXFzuvCM937dq1zmuOJPDg8+23IWAIGAJnzlTotZdf1ONP/kFrt+5V2alKZVVL7UoKNHJwX/3dvfdo5JhxcQUqqaQLYZIGDx6szp07u9fGNWvWCBI+d+7cBcW81/v+++9r3bp1LpzA6xjhDp6xd+9eHTp0SJMmTVLbtm0dYTdt2lTdu3fXkiVLnAfsn3HhofbDEDAEDIEAAh8cOqj//NlP9LsZS3Six2QVjBut7KIW7ordR/fojxte1Rtf+46+es+t+tJXv+acvsDtdf6ZVNL1UhKbbdGihYvr4uVGxl4JIZSVlWnZsmXu3NVXX62FCxc6wuVaPGC2xo0bu9AEcRi84Pz8fJ06dUpHjx71WdneEDAEDIG/QeCwI9yf6r9mrFX+tT9USbcrlJWVo6ys8/1I+W16qqrHCO1d+6r+4w+/VF5+vr70lQf/5jl1OZB2oxcg3PLychciwNMlrEDHGZ1D3lNmj2cMAUcSNn/768zbrUuRsHsMgYaPwIrlb+mp19co+6ovq7jPSGXn5ClL2RIr0VTLEXBOo8YqHjhJh3rcoSenztJbi+fHBZiUkW4kWXptIMqDBw/qnXfeESGF8ePHO4+WGC8b3ixeLeTMtWyefP3f/ll+z3Hu5b7g1lB6XL2efo++lgwBQyA6AocPHdBr89/SrsYDVDLoJlUT2Twf+fzoDeek3IJ8FfadoG3qpnlvzPvo+Tr+lZLwQixZIcE9e/a4EQgMrRk2bJgbXnPkyBE3lAxvlyFEeLKEFry3CwFDvPzNUI+ioiKXhSd2ricEwXlPSPxNKIJjPnGdP++PhWGPnsjt9WUf/B1GnSL1wQ5htY8vQ0G7hFkf9KDO+RSplz+ebnsv96ZNG/X6ktUq6PRJZTeSqsprkPScVNCik462uExrtq7S2fITyisorrEs+nxiPTWtSBdDEqsllkuHGCMRIFDG4e7atcuNcaQDDXJm7Obu3bvVq1cvN04QkqaDjes7dep0gXQY3wmR/+Y3v9HixYtFh5sHZf/+/a7wQLwQOkPRwkhQ3rjohS6QE28LYdYFndAF29PoHj9+3KsZ2r23D3vKW9gT9vE2CpJwuuoF7vDDrp27tGt/mfIGtLmoqCx8m53XSFVFbXXg6Gnt37tHRc1aOycuVv0iHzr4Y6WUk26wIGJAQgqMvR00aJAjDcICFNA333xT+/bt0+jRo51CjPWdM2eOmjRpojFjxrgxv7Nnz3YddNzLc9m4F6+YzjhGN+AJc5wwAxMsIHZInL8xSCwgYwGYbse9994QdOFthAH42I+wUkPwdOmvQA+GOIZZH+oJ9kGfwsJCF75Lt7oQKQ/1vrioSMXFRWqUl6tTlWdVm9XE3YLjVZXKz8t1dissKlZeXkVMriCfmlLKSZeCBzGyZ4MsINZRo0Y5coR0IRI2Kt6UKVPcuNyVK1dq6tSpeuKJJ/TUU0+5FpcON8btBj1diJxCATGTPKn6GWl4xx4k8g5zQg88Q/BEZ69rGHVCdl+xsRXE6+0URn28zN5G2CfM+nj7UN7QBcclFPpkZalLl64a2Luz5h7aqWZ/7Tvz9oncM5jhbPlx5R3boS6dCtW0WQtlu76hulNn3e+MlK4Of0OIPXr0cERKmACyIEG0PvHaQoVj1lnv3r1dS8M5fkPAzGzDA2YGGjHgAQMGuFuDBYDfvpD450bbc01DSF7XsOvj5Y/ch9VGwTKJDl6vsOoTKXdY9OnVu1TXjx6sN55erDNln1Bek2aqPoNBIjWSGNBwes8mNTn4lq64cYyy885PR6+PrikjXQogW5cuXdSxY0dHtJ50g4UTYoZ4fcgAQua1Bq+X4WSlpaXOy+UaQgTs8Zgjk8/PH/eetf+7Ie2D+DUkvUwXQyAeCOQXNNa4MVdp6MzZWjrrYXW67TvKaqTzxOszyJKy86XysjKVr/iTxrer0oTrbvJn67X/sAuyXo+p+82QJATKvqbk467BFgYCpqOMsADecNBDrulZds4QMAQyG4FBg4fqH+//O5Uef0M7n3tIp/e/L+XKjWbI/uvaSkc3rdKh6d/UiIL1+qdvfE1du/WIC2gp83SD0tfGM4t2TaT3Gnym/TYEDAFDIBYCuXl5umXyrSpu2lQ/+PFPtfSJj+tIt4mqbj9Y1VWVyt71poren68pV5bqW9/8noYMGRrrUZd8PC1I95KlthsMAUPAEKgnAhDvxInXqlfPnlqy5E2t27hF+w/MU1Z2lroO6qiBA/5Fw4cPV9t27eqZ00dvN9L9KB72lyFgCGQQAoQ1u/foqY6dOutMRblOHD/u+pqaNW/h+ogg5ngnI914I2rPMwQMgdAhQL8S/UZnK8/PUG1cWJgwHYx0EwatPdgQMATChAB9RNFGPsVbh5qHDMQ7tzR5Hi0aLRtDzCwZAoaAIZBMBDLO06UlY71d1uvlixSMDQ4OQ0sm+JaXIWAIZB4CGUW6TCeFaB9++GG98MILbsosi6k3hI8eZl7RNY0NgXAikFGki1cLwTJ92C+Ss3TpUjfDLZzmM6kNAUMgbAhkFOkSWiCe269fP/edNgiYb7Ax1diSIWAIGALJQCAjO9L8TLZos9ySAbrlYQgYApmLgJFu5treNDcEDIEUIJCRpJsCnC1LQ8AQMAQcAka6VhAMAUPAEEgiAka6SQTbsjIEDAFDwEjXyoAhYAgYAklEIGNJ10YuJLGUWVaGgCFwAYGMGqcL0bKUG1+Z4FPsfEmYr00YAV8oD/bDEDAEEoxARpEuEyP4ZPSKFSu0a9cubdq0SQcOHLCFbxJcyOzxhoAh8CECGUW6eLUVFRWaO3euXnzxRfcbb9dWG/uwQNgvQ8AQSCwCKSddXvchQ6biRlvLkhXAOM++srLyI6EAjrPxDEIEnK9pSi9rLxQWFuq+++7TJz/5SefxvvLKK877TSzM9nRDwBAwBM4jkFLShSxPnDihY8eOuRgrX/UNxlchWoiYlcEg05YtW37kq8HHjx/Xvn373DO4t02bNi5OG8u4PqbbqlUrt/DN3r17xcpjwTxj3WvHDQFDwBCIBwIpIV3Ilvjq4cOHNWPGDK1atUp33XWXRo0adcHr5Dxp48aNeuaZZ9xn1r/yla+4PSTJvXPmzNFrr70myBPCnTBhgj72sY+pXbt2zuutCSDI3Mi2JoTsnCFgCCQCgZSQ7qlTp5yHumjRIv3+9793oYPbb7/d7fFu8WrxbunoYt3bl19+WRMnTnT6c577lyxZotmzZ6tv3766++67tW3bNi1fvtyFG1i6EQ82WriCh3iy9ftEAGvPNAQMAUMgGgJJJV0fe4UwH3vsMTVr1swtsUiIgHgsyXvAjz/+uBYvXqwBAwa4a+jsgiQh3e3bt2vt2rXq3bu3brvtNpWWlmr37t0u9LBjxw537oorrnDXGrFGM7sdMwQMgVQhkFTShQDZevTo4bxTwgAQ7syZM91ncwAB75RxtKNHj1b//v3VqVMnvfrqq87z9SEBhnvt379fkydPVrdu3Zxn3Lp1a3c93vHmzZvd9+pTBarlawgYAoZALASSTroI0rVrV0eWeLWECPBevUcKsbK4+PDhw93HI/meGdf58+yPHDniOt/41A4ETbiBD00y4eHkyZM6ePBgLH3tuCFgCBgCKUUgZdOACTWQIFFPqEEkOA8Zk4KxWY4R8z1z5kzw8gvXEqbw5/z9H7nQ/jAEDAFDIIUIpIx0g0QaTX9PxtEIOXj9xc4Hr7XfhoAhYAikGoGkhhfioSwkS7iB0Qkk78168qXDzZ/jPMfxmjnmwxTcw9+EJrzHHQ/ZUv0M9ApuqZanvvk3JF3AAn2C+/rik+r7G6J9vI0SiW2oSBcCBRRiuSUlJW7dBOK5kCkhBSZZ+EkSXMtGrJcxvQw74yOUzEgjMZNt69atboyvB7isrOxCxfDHwrZnmjPhF+LeYU7YGZuyMQmGNTOwZ9gT+vCWR19FmPXBPj6Uhy7UpzDrQ7lCfuoPqb72YWRWrBQK0g22PvymI47JEAwp69Kli4YOHeomUfA5dUiVUQ8kQMSTZfovQ8nWrFnjZqxxnELCpAoqAJuPEwfzigVaOh9HD/Sjcoc9eV2w38XCUWHRFaIKVu6wyB1NzmC9aQhvjNiFMkei/vB3IlLKSZcKxYgD9tEID8VPnz7tRih4EDp37izG4U6fPt2N92UEBEPI8FSZRMH4XV9JabmaN2+ur3/96xeOASThhYULF+rZZ591+ULCTA+OJkMigE/EM9GZadVUbHQOsy7IzlsM+rAoEaEgb/9EYJeMZyI/Zd3bJ8z6ePtQNxk1xNtm2BOEi4dLYsmBRNknpUhBEniseKpt27a90Mp446E0xoREuY7fAEPIYNiwYa41YiowHi/jdJkGzPheCNW3WDyLAsKxIAn5mC5k64/zO8wJPfyG5+H1CqtO3nvyuoRdH8qzt4/fh9U2yB20j/8dZn2SZZ+UkS4KQox9+vRxY3YZmxvp0uMRQI433HCD81IhW0+mxcXFGjt2rIYMGeLiMHSg0eLyHH9NsAB4z9cf45po1/nzYd6DrSVDwBCoGwKJrj8pI10PB6QKUaJoNGXxCCBYUuR57ot87Yy8xudje0PAEDAE0gGBlJMuIFyMKGOd53isc+kArslgCBgChkAkAimbHBEpiP1tCBgChkAmIGCkmwlWNh0NAUMgbRAw0k0bU5gghoAhkAkIGOlmgpVNR0PAEEgbBDKWdK0DLm3KoAliCGQUAmkxeiFZiEO0TIBgfQbG9LJ+AxMujICTZQHLxxAwBDKKdBkTzEIwjz76qObPn++m/DH9mPG+lgwBQ8AQSAYCGUW6zErDs+3Zs6ebjcYiOHzaJ3K2WjKAtzwMAUMgMxHIqJgu04qZSsyn3j//+c+76cWs2YC3a8kQMAQMgWQgkFGk6wHF2yXUwHoNDWGhDq+X7Q0BQyD9EchI0qXjzG/pbyKT0BAwBBoSAhlJug3JgKaLIWAIhAsBI91w2cukNQQMgZAjYKQbcgOa+IaAIRAuBIx0w2Uvk9YQMARCjoCRbsgNaOIbAoZAuBDISNJlKjDDxtgsGQKGQN0QYLgldciGXV4afhlHugwV4yuzfDn4+PHjbmZa2D94eGkmt6sNgfggcLbitE6dOKrKM+XxeWCGPCWjXD0mRBw6dEg///nPNXXqVDdWl68M29oLGVLaTc16I3CmokIrli7W1GnTNWfRMh34oEydO7TRpGuu1sfv+IT6Xna5spRV73wa8gMyinSZBgzB3nTTTRo0aJA2btyoNWvW2DTghlzCTbe4IbBpw3o9/N8/1wtvblFZq6uUW3q/svIKtb78uNYtWK2nX/tH3X39lfrClx9Q27bt4pZvQ3tQWpMusSL/6u9nkLH3iXN+i3beX+f3fHKdqb98tn3kyJFasGCBdu/eLcjYkiFgCMRGYOf2bfrBj/9DTy8rU9HE/6umXQcpOytLysqWqqt0rmKK3l+/QD+b9v907Nj39d3/828qLm4S+4EZfCZtY7qQKat/sRgNW+RKYJ6MIdIzZ8642Cx29McvZtMgeV/sWjtvCGQyAsePHdETf3hKz6w8qaa3/EBFva5Udk6BlNVIUp7b5zZuppLBt+jc1Q9p6urjmv7c05kMWY26p52n68l2165dWrx4sdavX+96R/v27etWB+vUqZP7u7y8XOvWrdOiRYuct9q2bVt3nrABIYRIkg6i4L3imq4JXm+/DYFMRmDlihV69tU3pT53qXGnUlXzYlj1UUR4Ac3KkZr0ulJ7339HTzz/sq4aNUa9+vT/6IX2l9LK04VwIUQI9+WXX9bq1avVrFkzFRcX67333nPH9u7d68y2du1a/elPf9LWrVvVqlUrNxph2rRpevPNNy+EHMy+hoAhUD8EzlWe1YYNG7W7vEhN+oyTiO5FEK7PobpKymmUr7wOg7StrEqr3l7mT9k+gMAlebo1vbrH43WdGC5DuVatWuVCCpMnT9bll1/uYq7vvvuu3n777QvnVq5c6UIKU6ZM0VVXXaUNGzbohRdeEMe7d++url272md4Aoa2n4ZAXRBgtMKhsjKVF7RVkzZdznu5sR6Et5sl5TdrqfKsIu3ZvTPWlRl9vNak6ycURCNeH3utL/FCuoydPXjwoHr16qXRo0c74iTPoUOH6vDhw9q5c6c7tmfPHnd+2LBhaty4sXr37u3CC/PmzRNecLdu3ZzHW1+ZMrp0mPIZjwD1p+pclaqzclz4QBdZ7991c2dnqUpZF/pZMh7ECAAuSroQIaRK/HTZsmXuG2N+VAEGoeefOOv48ePFVxjqMxKA5xGPhUT5lM6WLVs0YMAAlz9hhPfff999UBJihoC7dOni/qYjjXsYc3vixAl3XbTGIUJ3+9MQMAQugkBefp5KmjZRozObdfbIMeUVN5VqGuxTLVWeOKmi6nK1at3mIk/PzNM1ki7ExcgBxrPy6s6YViYYQLoQJBvnIboRI0bUeuRALKgZidC8eXNHtOT3m9/8xnm4EDnfMoOQIXdivceOHXOf3sEDRw5k4ndFRYVOnjzpskB+zlkyBAyBuiGQl1+g7t26qOTMTB3ZvEgth9+oqhik+9fRYzq9b726555U/4GD65ZpA7+rRtJlXjUzuF599VXnPX7pS19S//79nTfryYw9RMwnzSHg+iSexTfMOnTooMLCQjeOllgt5AkhX3PNNWrfvr0LH/A313s5fL7RjvlztjcEDIFLR+CK4Vfq5tHz9MvFU1XSZ6xyi4tUxczf4MQzhuzmSSd2bVXTvYt11/WjNHT4yEvPLAPuqJF08R7xHImx8upOh1VRUVHUEEIk+dUFO/LDa8ajZn2Eu+66S2PHjnWPIrRByIFzeL4QPWTMFkx4u2zBxDU8O3gtDUrkdcF7wvw7qGeY9TDZ0wOBtu076u/v+aQ2bPuJ3vjzQ2p70zdV0K6dqircvAhl5Z7vQDuxZbWOz/p3TelTpU/d863zB9NDhUuSItH1p0bSJZaL59mxY0c3AYGxsQzhihQKwoUI60u8kOAHH3zgwhmlpaVi9AIkT36Q/uuvvy5GMTRp0sTJATGTL+fZE9slBFFSUuJARh7O4RUzKoIGhL/Z0IvGhHv4m+SfdUkWSqOL0Reb+Q296muTVKmH7OgR1CmsungMvS7s/W9/Lp33OCxDrxiu7/2vr+pf//2/NOuRu5Q/4DYV979OOU1aqfLwTh1fPUN521/X3eP669v/9I/q1KVLqDrSKG/+7Rlb+LJXV7vU5NBdlHQhPYZfzZ07V88884zGjRvnCgwCkig8XMNrP51ZCFufhIEhRL9kHB5tMPlGYNu2bS6227NnTyffvn37HFkjS48ePZxc3Mf9dMA9/PDDWrhwoQuDIDP5HDhwwJ33hA3hewIO5hmm39gFG9CghD2hB/ocOXLE2Svs+iC/r9g09mFK1JfS0n76P9/5J42bPUcLli7SptkzdPzUGbUqLtC4Hu107e2fdvzQsnVrUR/DluAF73jVN1Tarl3stSeyqskpRoKsIKInn3zSES5eZIsWLdzV3MZG4Rk4cKDuv/9+QYD1KUwYFm+a8bjMRkNwho0BwNKlS92kiRtuuMHlM3PmTNcQEOcdNWqUI+BZs2a5mDNhCTxyKq1vwQhb4OmSBwnyZiIFHXb33HOP7rzzzlC1zNFMhj3QE7zokAxzA4Lsp0+fdkMI6S+g7NVQVKPBkXbHkJ9OXoiX8hk2fbAJMldUlKuivELHTxxX+elTatq0RAUFjVXQuED5+eedpLDpRmHBLnTQk1q2bFkvB7LOni5C4L3eeOONbpEYhPFExm+A5W8KEGRMK1GfxLPwTC+77DIX06UDb/r06Y4oIfRrr71WTAdmhhpES4Pw0ksv6emnn3bHGLM7ceJERzjI7mWEaJHRJwoPpAsxsQCOJ6eagPL3pvMee6AL+qKL1yudZa5JNvTw+vjGsqbr0/0c9kEPynmY9SksLJLbiopcPSWcF2Z9guWG8ua3RPFBjeEFCgnkRHy1T58+TjaORUsUJLZ4JGK2w4cPd60NU4IxKGOBmTBBIwChEme+/fbb3RKNjNnFG+I8Ix+iyRF5LJ7yxkPneD4jlo3imYc9yxCgDlEX2TcU0sWqia4/NZKuL1YIkWhBgnnxG+JlCjChC5JvfbwcGJnwAwvd+MQ1JH+NP257Q8AQMATSBYFak24qBIZEgy5+NDINtrDRzqdCbsvTEDAEDIFYCNSKdGPdnOjjtSHR2lyTaDnt+YaAIWAI1BaBtFrasbZC23WGgCFgCIQVASPdsFrO5DYEDIFQIpCxpGthiVCWVxPaEAg9Amkd000EunTOMRaY0REsqkNHnBFwIpC2ZxoChkA0BDKKdCFYZszx3TWmyfIJIKaYMuXYkiFgCBgCyUAgo9iG4WeQ7ooVK7RkyRI3o41Fc4x0k1HULA9DwBAAgYwiXaYpM6ON76qxQbx8zLI+60VYMTIEDAFD4FIQyCjSJXZLTJeVyFhAhanDeLkW072UImPXGgKGQH0QyMjRC8E54/UBz+41BAwBQ+BSEchI0r1UkOx6Q8AQMATihYCRbryQtOcYAoaAIVALBIx0awGSXWIIGAKGQLwQMNKNF5L2HEPAEDAEaoGAkW4tQLJLDAFDwBCIFwJGuvFC0p5jCBgChkAtEDDSrQVIdokhYAgYAvFCIKMmRwAakyP47hsft2R2mi14E6+iZM8xBAyB2iCQUaTLl3+PHz/upv7ymff9+/e79RdYdcySIWAIGALJQCCjSBcvl9lorDC2ZcuWC9+4D35nLRmgWx6GgCGQuQikHen69RHwSiNX/4I0+eRzRUWFsxirhnEdx7mPBW04H2stBRa2IaTw2c9+Vp///Oe1ePFiPfvssxeel7nFwDQ3BAyBZCGQdqSL1wmprl27Vps3b3Yk6j1UyLRz584aMmSII8+9e/dq3bp1LkTQrFkz9enTRx07drxAwtFA5FnEdFnwhs1iutFQsmOJQiCWQ5Co/Oy56YdA2pEu3i2x1meeeUbz5s1Tt27dHIl6L3bUqFHq37+/ysrK9Pzzz2vlypUqLy93X4EYMGCAbr75ZvXr1895vbEKuF/wBq/YkiGQLARo8PlaCWXZUuYikHakS8EkDHD69GlBsA8++KDzdj1B8pkdfkPIGzZs0I033qiRI0dq48aNev31193x1q1bq3nz5jHDDJlrbtM8VQhUVZ3Tls2btHnTJtev0K//AHXr0VPZWVmpEsnyTRECaUe64ICHSrwW8iwtLXWF1Hu6nMO7JfQwbNgwjR8/Xp06dVJJSYnrGHv33Xe1Zs0ajRs3rsYwQ4rwtmwzDAHK64J5c/To7x7Rqve2qOzkGVe+WzZprGGD+uizf/85jRozNsNQyWx105J0vbe7a9cuMbSLxILjbdu2dZ1rxHIPHTqk6667Tu3bt3eeMaTbs2dPLV26VNu2bXNknNmmNe1TjcCRssN65De/1K+eeU0HWo5R/vC/V05JO0aLa8eRXdq8ea4WfeOf9aU7r9cXvvyACouKUi2y5Z8EBNKOdPEM6ODCy507d67++Z//2Xm9vXv31qRJkzR06FAXemC8LV+AYPTC2bNn3Rd+GW9LWIKPTVoyBFKJQHn5af3xqaf0oz+8oTNX/k+VDLpJWfzLzpWqpeoO/VRVOlZ7Vr+snz3ziAqLm+gL9381lSJb3klCIO1IlzACXuunPvUpTZgwwcHAaIbVq1dr5syZjmTpCMMbhqDZgom/OU/y1wTP229DIBkILJr/hn47fYFOD/mCWgy9zREtZOs2ymZ2jnIbFanpkFtVVlmu3z7/Z/Up7a2x11yXDPEsjxQikHakC2nivXbv3l09evS4QJzEbWfMmKGFCxc6D5dhXyRPrNzHb79FYsrQMD88jGuIGbNZMgTijcDhQwf00mtz9M4HjdXxuutFX1l15EAZvN1qKbtRngr7jNHGHfM1/YUZGjt+opRt5TLeNkmn56Ud6XpwIEYSZAo5dunSRS1atBAdZX379hWjGPBoOe/JlFENkDETIPy97of0kWE6npjxqj1ZR17v7wvL3uMVKS/6hTEF9fE6+H0664PcB/bt0frNu5Tbfrjympao6mxsiasrpbxmXXSqw3Bt2fWq9u59X+07dvmbN7jYT0jNGV+HotkpNRLVL9egHv5J9Slv0Z7nn5u2pAuBesMiLCEGNki1TZs2OnDggLZv3+5GN9DJdvLkSfOgInkAACAASURBVDe+lzgvEyQ8YMR59+3bpyeeeELLli1zC93wPIh6z549Lh5MXhDw4cOHXZ4enLDt0Rk9aIyY6lyT4cOgm7fL0aNHdeLEiTCIrPxGjbR79y4dOnpC+R3bKIsXsjM1iI63m5+t7JI2Ktt2Srt37VRRk+YiJpzu9sM+3kbUp7An6g/9QyTqT10Tz4GjYqW0I1282mPHjrlhYQAwYsQI10kGYbJewuDBg3X55Zc70n3jjTeccmPGjHHjdOl4wwPmPAnlKRR0zDG8DCD84jZMwmA2GzPfyJO/Gbie7gU9liH98VOnTjmdG4IujNemAcF+NLbYM90T5auwcaFyc7JVfa7qw1juxYbjVmcrLzdHRYWFKioqVHb2+VBZuupLPcE+TEzizbIhhOr8mzOY47zVtbxd7L60I10UxqAQ7/z58/XSSy85r5Q472WXXeaGguHJDh8+XDt27NBjjz3mZq/hBTMVmAkVxH8BkITnBwGNHfvRsZBUjgULFjgv2IME0GFO6IG+NFZhJ13KgK/Y2IqK7e2UzjZC5jbt2qlNy6Y6fWC7qvBycQJjtBdZOVJVebkqD25SsyaN1bZ9B0dg6V4WvX18/cJpCYN9YpUd9EEXGhIS9SdR+qQd6XrPBm8VEIjhcowpvsw8Y6wuALHOwsc//nEtWbJEjNul0w2veODAge68J10ABDxfSDzo/m/2PgV/+2Nh3EfTLax6ILe3i9+nuy7tOnTSsAGlmjn1PVUcPqCClm1UxRpNHxa1D1XIkU7v3aH8/cs15Preatmacbwf6vzhhen/Kyz2iYVkpPyRf8e671KPpx3pQpDEhzp06ODG6k6cONHphKfLRoJQ8X7wfJmxRgiB1xvO0+IGCdcDwnODLRfXRLvOXx/mfVDPMOsRVtmLm5Roym2Ttfid9Zr1xq/UYcp3lZ0vVUd0qHGs8vRpnXp7mq5uXa5PfuozYVXZ5L4EBNI2+k0rA7ESo2Xjd2TLA8HyGkZHGntPypegv11qCCQEgX4DBupLn7ldvcvm6P3nvqPyg/ulPCm74PxWnSud2LNTe6f/i/ocm6Ov33+fevXplxBZ7KHphUDaebpBeCK90+A5fl/sfOT19rchkCwEePO6dcrtatGqlf7l+z/W4kcn61yPjymn6yje1XRux2LlbnlFHxvYSd/6h29r7PjxyRLN8kkxAmlNuinGxrI3BOqFQFZWtsaMGatf/6Kj5s9foHff26ADh6Y6Z6H98Da67O8e1NixV6tb9x71ysduDhcCRrrhspdJGzIE6J/o1au3OnfuorNnKnTi+HGdrTyrFi1aKTcv78IQxpCpZeLWAwEj3XqAZ7caArVFgD4JtuycXJ2trFRRcXFtb7XrGhgCaduRlkic6ZDDA2kIs2gSiZM9O74I0AfBSJsq+2JJfIEN2dMyknQZ/8tMGgZCUxEiR0WEzIYmriFgCIQIgYwKLzCVlPUVfve73+mVV15xa+8y84RpppYMAUPAEEgGAhlFun56LJ9gv+eee/TWW2/pxRdfdF5vMsC2PAwBQ8AQyCjSJZRAHJc1GujUaNWqlZtQwXFLhoAhYAgkA4GMjOn6KcANdRpwMgqO5WEIGAJ1QyAjSbduUNldhoAhYAjUH4GMCi/UHy57QjIRYDlHv4hRMvO1vAyBRCJgpJtIdO3ZdULgxPFjWvDGXM2fN1d79u5Rxw4dNG78Ne77YY1DvuZxnQCxmxoUAka6Dcqc4VamoqJcL74wVb/+3ZNadzhPJ5v0VmWj/srZe0R/eOPXGtT2N/r8vZ/WLbff2SC+VBBua5n0dUXASLeuyNl9cUWgorxcTzzxuP7vw7/Xke4fV5NbP6XCAr7kwcrf1ao8eVjzlv1J677/sA6WHdEXvvjluOZvDzMEkoWAkW6ykLZ8YiJQea5S06c9px89Mk1Hhjyg5sPvVJb7xs2Ht+QUNFGza7+ug8u76GePPa5WJcWactc9H15gvwyBkCCQsaMXbGxu+pTQ3du2avor87WzZISaXXHH+TUxGDod3KqknPxGajp4kna1GKtpL8/TyWNl6aOESWII1BKBjCNd1lmgV7ykpMR9bYLFpo2Aa1laEnTZ+g0btHx3hYouv1m5BTmqPhc9o+pKKbe4RPl9JurtvVWaO+f16BfaUUMgjRHIqPACs9FY5IaPXe7bt0/r16/XBx984L6rlsY2auCiVWv3voPadSJfrdr2EcRaY6qW8kvaac+pPC1fsVI333ZHjZfbSUMg3RDIKNJlzCefdv/LX/6iF154wX1tmCnBLIRjKUUIVFfpdMUZVVTlK6egqaqrLiJHtZSd10jlVTk6cuTIRS6204ZA+iGQlqRLCIDXfr/mLa//TNllScZgKIDzfJySPedZq5QtVsLLZVWx++67T3feeafefvttzZo1SxUVfB/bUkoQyMpWYUG+GmWfUeXpo8pr0qxm4s2Szp0tV+PsSrVo3jolIlumhkB9EEhL0oVcjx496rxSCBES5ou/zZs3dyTriff06dMuPHDq1Cm3PGOLFi1cnNafjwSG4xB0+/bt3YI3hBaI79oaDJFIJfPvLHXt2E49mpzRnj3r1XzAVec/Vc5IsWgpS6o4vF9dis5o9KiR0a6wY4ZAWiOQVqQLueKNbtq0SQsXLtTKlSt14MAB9/o/cOBA3XTTTRo0aNAFwpw3b55bF3f37t2OSCdOnKhrr73WrR4GccdKkC9EG4ucY91nxxODQO/SPhraqZHWr3hOTXteqey87L+N7VZLWfnS2RNHVLnuRQ3rmK2RY8YmRiB7qiGQQATSinQJKRBzXb58uXbu3Klhw4Y5MoUgt23bpjlz5jjC7dWrl1sLl4XIu3XrpltuucVdv2TJEufJTp48ucYlGz3Z+n0C8bVH1wKBLt166O7bb9Lyf/2Fts7+pdpf91VlN5IbxUCMNytLysqVzp4+q0MLfq/eRxfprq99XYXFTWvxdLvEEEgvBNKKdInHFhcX6+qrr9aIESPUrl07NWnSxIUXdu3apZkzZ2ru3LkinMDIAwh3ypQp6tu3r/B26SjbvHmz3nvvPQ0ZMsS82fQqazGl4Q3nuhtv0vfPnNVD//af2vD4ajUb+2UVteutnPwCVZ45rRO739WxRY9oYPZ6/cu3/qeuv+nWmM+zE4ZAOiOQVqSL58ni4t27d3eYURlJdJYRh+WzOuvWrROxW+KxY8eOVc+ePV2YoG3btrrsssvcyISNGzdq6NCh6Yy7yRaBAA3mzTffolYtW+qPz07VvDe/oy1HclR5Lle52WfUq3m1PjOyp+76xL9q1JgxEXfbn4ZAeBBIK9KNhM2//hNewLslTkuH2smTJ1VWVqaWLVu6jjA61Bj25c8dPHgw8lH2dwgQaFRQoDFjx2ngoEHauWO7Nm7a7BpXvvDRq3dvde/WTU2althiNyGwpYkYG4G0Jl3EZrQBYQcmNPBRyXHjxmnPnj2OeDnnvWH2bBCzHwLG3564Y0NgZ9IJAeL6LVq2UvMWLVXap69rbIuKilTQuPCCrdNJXpPFELhUBNJ6GjCkStqwYYMbyUAMl1gt4QY/OiGSVCP/vlRAwnw9jQzTm3kD4HeYE/Jn5+SqmqVvcnJDr0+YbWGyxxeBtPV0IVaGj73zzjtavHix2rRpo2uuueZCxxrhBCqmJxdPttwXOcOMa4gV+3UW/N+M0fXEHl9Yk/+0Qwf3a86sV7XsrbccbpcPHqIbJt2sDp06J1+YOOWITRvS0D5fVv0+TjCl7DHo4beUCRHHjJOlS1qSLuRIDJdxuswa69Spk0aPHu1GM1AR8eYY1XDo0CF3HUTL59WPHz/uRj+0bn1+phLX0kHDdFE+tc7IBoiW49zDeGBGPfjEdWGpEMjZKL+RDuzfq+eeeVp/njlHW0401qm81qpSlgqXvqpf/f7PmjzxKn36nnvVuWt3hxW6hyGhH40ubzTE8PkdFtlrwpfQF3pQVmlQwpqwD3UOu6BLWOpNTXhjFz8Zi6Gr9SlvcFSslHaki/GYjbZq1SpHkoxCuOqqq9z0XUAgvtu1a1fn+TIut0uXLrr88svdtYzvZZpvv379HGBcD4EDJM/jesiahIfLojecp/BTucvLy0NTeBo1KtCGDe/pxz/+D01bvk8FY7+h/O6j1CTnfFih+tw5bd31jv596n9pydIH9J3//R0NuGyQ0zFWYUi349iFzZNvuslXF3kov5RLOn/rU6nrkne878E26BOmelMTBp5fuAad6mOfmkg3q7qGJ+/YsaMmGeN+Du+ToWBTp07VjBkznGc7cuRIFxqgVcXIDCeDZPGAp02bJrzaHj16OI917969Gj9+vCZNmuRCDF419txPAfEtMiGIRYsW6bnnntOnP/1ptxYD58OQaCgO7NunH//sP/Wr2dtUMPHbatx5kLKq/zaOW75vvcoX/LfuLC3Xv//wB2rRqo3DId31xE4Q04kTJ1xDyXBBb890lz2afOiD/HjtNPBMaac8hzV5+2AjRg1Rd8NuH+o/Dh+JfpH62Ic6GiullaeLIWlhIF5IktEKs2fPdsakoALKqFGjHOleeeWV7nWZWWovvfSSI18mVbBRQYMEynM5xp7EHtLFKwYcf7wmoGIBmKrjC+fP0Z9nvy0N+ZqKul9+fr2CyMhBltS4U19VXnGPZi37ua6eMV1/9/dfdDqnSu5LydfH29n735dyf7pdCylR1vwWpvIWDUtvE7NPNHRiH0sr0oVYaWHuvfde3XHHHa5wBlsbCi1EyRAiCuyECRPcaAaIGhJlmUbOBQnXqx58Dse4P9p1/vp03pd9cFAr1mzQgcL+KulzjYSDHkm4KMCxKqlxx8tVtmWYXp27UJNuuVWtWrdNZ/VMNkMgpQgk2mNPK9JFWV5TCBl47zMS/SAgEDBbMAXPB483pN8njx3R+0fP6ky7ocorbnzey42hIF9hyGnUWGrWTVt2zdHGDeuNdGNgZYcNgWQgkFakG1S4NuRZm2uCz2wovyvPnlH5uRxVF7dWVo5UfaZmzbhGjYp0ovysjv81ZlXzHXbWEDAEEoVAWk+OSJTSYX9uTm6eGmVXKfv0kfMLfv9t/9lHVHRfY6gsV0F+rgqL+Ky5JUPAEEgVAka6qUK+HvkWNilRu+Js5e57W2dPVUo1kW62dI4xrmU71b1dc/Xt178eOduthoAhUF8EjHTri2AK7m/Zuq0GD+il4kNv69imhcouiC1Edp5Uvn+jSg4u1XVjR6h12/axL7YzhoAhkHAEjHQTDnFiMhg/YaLunDBQFYt+pRM7tiu78fmFvoVF/7roN2R8eu8enZz3sK7uIt16+ycSI4w91RAwBGqNQMaSbtg74dp37KSvPfAVfXp4Ux1++nM6MP95VRw7en6YWJZ05vhxHVzyF33wzJd0fYcP9O1v/ZPatOtQ64JhFxoChkBiEEjb0QuJUBeiZSA3X6dgmh7jesM8k6ZX71J97zvfUp+ez2jaq49q/dqntC/7/LoThecOqbTJKU2+80p95tOfUe/S0kRAas80BAyBS0Qgo0iXCRRM83vyySe1YMECtxAO6zIwWy2sqWu37nrggf+hKbfdqo2bNmnnrp2qPHtWnTt3UWlpbzdturCoOKzqmdyGQINDIKNI13u6TL4oLS3V+++/7xZED3uooai4WH369VWPnj118uQJN2ec+fAMLYs1yaTBlWRTyBAICQIZRbpMM2ZdXT7TfsMNN7gFb5599lm3ilVI7FWDmFnKzctzRFt19qxy8/JruNZOGQKGQKoQyLiONDw/1thlXV0I2C/akSoDxDtf1phgC7v3Hm9c7HmGQLogkHGkC/AQkiendDGEyWEIGAKZgUBGkm5mmNa0NAQMgXREIKNiurEM0FA6m9CDIXCkhqATy28SCgr7urO+3AXt44+Fee/t48tcmHVBdvRJhi4ZTbrEc1ksnUXTGUpWVlaWkHKDMcmLjrxExVqp0Dybb8uxTjCfJfLH4q0UuqAT+aFTIhKyM5yPLxOwfCfx98g1keORL/mgT7Ls4z/Tw1jxROgDJl4nH0aLB06RzyAPPqPEWtbYJ5Hj3Slr5JeosuYxwx58qYS84IP62Icvl8dKGUu6FEgqMoT7/e9/X3/4wx8cAccCqj7HKZgUGAqnJ6v6PC/WvejkPwfD5A8KT7yTL/yQOxUNncg33ol8wA19IChslYh8kBsipPElH8g3UQn5wY3KjH3qU6ljyQhuNLpgR1lL1GeOyIdGEX3ALZEeIrpgH/99w1i61/c4uHnSxT71KW9vvvlmTHEylnR9oeFbVZ/4xCd0++23O0+X4/FKvgJPnz5dK1as0De+8Q23QDuFNZ75IC+FHvJ44oknxLftvvvd7zpCxBuJV14UQr7M8d577+nnP/+5Bg0apC9/+cuugtengEbDm9Elr732mh577DF98YtfdMP84v3VWUgJfJ566in3zb2HHnrIfegUIokXZl43ygJ2f/75591nqMiLN6t45oMNINmdO3fqz3/+sxuLfttttzki8XLEY08+EO38+fNF2cY+PXv2jPvQS48NuvBNxO9973tOPwjYn4uXPjTqfGORcs0kqh/84Adxx83LmrGkCwAUHioDEwnatGnjPIN4GZNnU6lJ3sPlU0StWrVylS9e+Xg9iH1CFpAiBYh8yDfepEtlY/o0upEPE03IF33jpRPPQnbsQh54HejD73jmQUMFPv77eTTA6IN3Ha98vH3AC48N/Ggc413efD40VjRO6ERe6BNP3Hw+PNvbp0WLFnEv175ukh9lAVtRf+Jdpr0+YESjCH7UJXADw7okZK8pZTTp+orFax6vFmz+WE2g1facJyI+GU/rTMVjn4jXSi8/ebLxN/nEOy8KJsQ+evRo5xXyN3nFO/FMrwt7b6N42sfH2JmdiG3wcNAn3ph5bLw9vH3QMZ76kA+NCATSv39/dejQISH6ePnRJ2ibeOPGs0nER315SFT9CdrG65eIco0+GU26zqIJ/A/jsQ0dOtR9wZhKnejOgASq4x5NpcbrvPvuu91bAn+HNVHRIL0xY8a4r0xjnzDrgx0gJd4MJk6c6OyDdx3vFK2hiHasvvl60r3iiitcHaJhTBQRBmVNhC7B52c06WJU31oHQYn3b15X2Hwhivfz/fO8PvH2OPzz2ZMHIRlew/zfwfPx+k3BRw8aqUTqg7yQLSnR9vF5JDofsMPb9fm5H3H+zxNTMupPsuyDXSB1Nq9fnGFzj8tY0gVgYjbt2rVzsa9EtqCJrmS+YFBQiK/5mGQi803ks9GHykzcsHPnzi6cwd+JqgiJ1iVoH+Lh6JLoip1ondCBhrdt27bOoeDvRKVE64Lc5EHcGH3YJ5IPsqpr0Ihe8DAnKqmvqKgZVJXjxO8gKAoPAXpfsYP3eIOkGw7IGNTHy4k+eIe8YuKRcg17nyJx8MdTsa9JLvTj1ZghPJAvDSSyczxon0gMUqGHzzNSH44H5eM3nY6UM+zjicrf56/1e//cdNkHyxy/qT/ow1AuiAq5w2KfIKYeb+qNHyFD4xhNn0ibBp8T/E0/TqzUYEkX41OY2ZMAkM0XdA9I8Hy0e7jeG8Xfk+q91yuabJH6eJ1qwiDZ+iBTUC4vW6Q+/jpvO/T2BMU9XM+WDsnbBJlJXuZI+YLnuS6oky+f6VbegrYKeoCRuvjr/HFvz3TQx+PsZfNlBtnQycvIdfxm49qgThyrbZmriXQbZHgB4I4cOaKlS5dq2bJlDijGlF599dWuEyhYcILgHjhwQIsXL9aqVatcnG/48OG66qqr3NAYX4C8sVKxRy8Kwfbt2/Xuu++qV69e6tu370cKDfqQuJZOIa5jwfaDBw+60Qbjxo1T79693TX+2mTqQp7YhrG+4AzmxOwGDBjgsG7fvr2zF9f5zRd+xlEuXLhQa9eudW8nV155pbuH0RRBmyZTH2QD523btrnytnXrVic/Pe4jR45Unz593MgIT74ec+yDJw8G6AQmPXr00Pjx411vPTr4a5OpT2Re6MfsLMbJIg+djrx1BImKazi3a9cuN3Z3w4YNzpOn7tAJxptkKu2DbJS3V155xU2GokOORKcj4YSbbrrJ1aPgyAjsw1vjO++845aA5TejXKg/nTp1ulA2I/Gqzd8532PEcYwE2GFLAMqg81dffVWvv/66GxPJawOVAn2oDIQSggWaew4dOqSZM2c6gqKA8Nq0ZcsWVzG4h46J4D3JxgUZ2TZt2qRf//rXmjVrlisEVOrIAk0l4Njy5cvdYPx9+/Y5sma/e/duN96RwpZsfZD/2LFjeuONN5xtmA2IbSCtPXv2uFACpAuJetnQhQrAgvPTpk0TM304RiXApuiJVwFx+3uSZRvkIFFOXnrpJa1Zs8bpgp7It3//fqcLYz79tVyPPlRwHAImF1D2SOgIcTGGly3Z+jghAv+hBzLQaP/iF79wdYmhgkESRS82JmRgH8iZvwkLgQv3U3/8swKPT8pPsKbBmzt3rv70pz85e9BoEBqh3KELZArevmFEVs7TGM6YMcM1iOiBjjT8kC59J/76aIoQnoiVGpSni7EpzLS0FGgq47333usC/VQKWi28CTwQRhMAGvcwWJ1zq1ev1uDBg3XnnXe6SjN16lT3HGbbDBkyxF2b7IqAfGyQ0pIlS5xnhKfnZY80rL+ewrFo0SJXsO677z5ddtllblbciy++6IiLDkQKTiRhRz4v3n97ufv166cRI0Y47xubMWOPRgIdr7vuOudN+WshsJUrVzpvBe/2jjvucA0olZy3GWzKuFR0T7Z9yI+NSnv55Zdr4MCBLgaNvai06MQkAogHrL2MkCtvVVTw+++/351H97/85S9666231LFjx4R38NZkW+QEfxpq6gbyUoY4HkyQGnFQ9IRkGap28803O3J67rnnnD0hNWzkdQ/en4zf6EEZQ4YHH3zQfcKKOk9CfkiY8yRkxE406NgDUv7sZz/rPGKIG2cHbqHu+H4gd+Ml/NegPF0KMJ4UFZFWjNcGXsEBjmA/r9i8znKMigC4dABQQWjNAZF7aMnwtujAgbx4JgUnFd4uhYCCQaGHRJF72LBhrpDQqEBeQeLkWv7G66LxGTt2rCAq9GejsFGg8L66dOnykXsvodzU6VLICY+UEQmQJF4ttgFrSAsd169f7xo+sKeyYFM8QAiKayZNmuTu4x7sgfeBToRM+Jt7kp2wCfl3797dvVajI2OZadgJ71DGOO/1oWxScSGpa665xtkTfbEPIQeIDmyC3leydUJm3gznzZvn5KHjD8zxdH14gbLJht14A6HeXH/99a5sUZewB3WLtxn0951tydQF+cAdR4U3jxtvvPHCmxF6YCPqjE+UN95y0QfZ0YfGFH3AAAeAAQbYhy1Y9/wz2Nfk6X6YW/COkP4GPAotxApAECWJyo5nxzEqKaB6oDEKLTUVm2mg3iMBfMgBsAGZ1w2uTXZCdgyLXJ/73OfcRnwauWIZnHtoYGi9IWUqNL8pCODA6ywYeQySqRN5eoIBY0+SEBX4YhuOeazZU/nRh0IODlRiKjAzrtgT44bI/D3J1Ie8kB3ChGSQgb+REbnRl4YFm5A4j35UaMqqb8yxD94TxEV8l9AL+KRCJ2RGns2bN7v6gpNCI4nc3l4eY+Tz8uKdYyNsAQbUH0iNOhe0qb83WXuPIaG12bNnu5AB60bgUGGXYD3gWuo6DQnnCN+hA3UNRwX94ArKI/f5Z1+KLg0qvIDigIPng9FpyXxhBzgAwmulQniw2FNIIF4SFcdXYO7hfs7xXH/PpQAcr2vRBaJFJiqj1yvy+V5GMKDi4J34YxAUG+cgN3888hmJ/jsoOwWXCglxQjQUcvT0lRQZsQceBrKjv7cfv7EL9vHXJ1r2aM/3+iAr/Qnr1q3Txo0bnVw0kHhKyEniGmQFf/TCrj55/aj0EHKq7INN8LbxxvHi8W4Je3g9vbxeH/Twdc7bBNmpg6RU2geZkYXGDKcDPag/1AtCiYSygqEPbx/KG/UnaB/uYyNejb51tU+DI11AplD7AuELCgB5QN3JwH9cQ6Vg76/3p/k7+Dx/PNl7LweyRMoYTRZ/fbRztX1GtHvjfYwKjtdASIjfhEPwhCMbuaDOvrBzrCY94y3rxZ6HXHhBf/zjH10jgi545j6UFbwfG/hyFTzOM1KpE6QCSRJXZs9HXHlDhIBiJW8Hf56/fYqlpz+f6D2ygCmjKCBXrweNPCFFVrK79dZb3VsTjTnJ6+P18OXNyxrruD9/sX2DI10UBqRIoDwQ0Y5zjAof7b7gOQ+2f1ay974w1JSvv8brEk1mr2tNz0n0OeSjguMZ+iFtweFSkfl7fTgeqVPwXOR9yfobmSAY4uwPPPCAi5szfIwhYZAuK2QF5a5JZs5ho1QkZKThwFOnwaCzk/CB9/J4E8Qjx7v1KVIX/vYplbp4Gdj7kBa/kYn+DEiWsoeuhEI86Xp9gnoEnxU8HrRp8JqafqfGsjVJVI9zAECB4NWBCsArnE+0cJyn1eYagOP1h9chChIxOZKP3XIt91D4qTQUuroA7POPxz5o7MjncQ69fKUgjoh+YIDcnKdQsfH6zpYqfTzpU7kZO0nMD8KldxycsR3yYhuvE/JiDzbOITu6cB6b8sxU6uPLFJWbsdMf+9jHxDhviJdOHPTiGl/muI5X12AYAX18yCEYB460daL+Rj5vExpD+jiQn2GKhw8fduQLQXENWPuyxh77ILsnY87zG1tRf7BPKhNy+DJC+QJ/+jfAn0aFc5Q3bx/4gN+c9+WK+9jQB319Ob1UvRqUpws4FFZ6fekZpvee1wrAoaAQM6T1hpSJyVCwqAz8jYfCeXr26XyiwPAKwisW92AAD/6lgpyM69GROBSFhMpMwB+ZGcXAb+JZdJ7RgYPXRYHzccZkyOfz8IRJ5ySdGaTJkyc7/D3hcozGj4pORaACoAOdG9iVuC/2oWMEEmbUANeBQSoSmCMHuLOhIxu/qczIyVBzCQAAB3BJREFURdmhYw25sQueFWWN+C8dUFxLxw4NEI2IH86XzDKHzJQhRlww3tZPEkI3yg6yIzNxUIZiUjfQD3npZMKmlC/swXOoP9iRjjiPQyrsQ57YiPIOP9BIIBdhLXSm/nMOPqDhI8EH6AwW6IbNKH9s2ItjdS1vDWrIGGBR+SgcdAJAtBAmhYNxurTaDNGhx5gxuT/60Y/ckBj+plIzTATiBXA6EvzAdQoZgfhkVgBn+Yj/KCAQEwUbMqXiMpOLRCOCvA8//LAjADpvqMDoxEQIChbDriA6PDHGKie7IUF+KjCVmVgaujDDCfmwmfcqsCGF/ac//akbJkfPOd4FstOJgU0hXMYcU7lvuOEG14gk2z7oQ57IysQaZANnKiMNPsOt8KjoiKJS80mo3/72tw53lvukPDIGlgYQW3A9Y0Hx+HmtB59k6wT2lH+8dGRguCHyYB8aP8iWY5Stn/zkJ64eoQuJccnoDinRODKxAHsz7CoyvOJuSMJ/3kYMRQRf8MRLZYYaY25p3CZMmODI9tFHH3X2oQFkWCYNoq9nPIfJVozdpe5wnoYkln1qGjLW4DxdCiokSicGw0O+/e1vu9aMAkMFZ/A6BZxWjQH5FDI+10NBohIwW+of/uEfXHEAODoSeB4Ap8IzjFUuKQS+QLGnhfYki2fB54d4Zae1ZgYblQFdqUCQAN5JsvXBNsjzwgsvuI1Ggw4bZEN+9tiIig2B4W1hq7vuustNTsE+NBwUfHTmjYYGEc+KFKsCxMIwHscpFzQIkAuTAR5//HEnM5UZj5yp55AQDSVDsGgEmWhD5w1TSvkUDY0LCV0pn0yfhby91xUPOWvzDPCnkQgSCiEH3jgoW3iGhE0oO0wcwnbERrkPksbTnTNnjgsZYWsaEwgXO5NSYR/yxUZ4t74u0IBAvDgfEC7y4cESOqF8of+UKVOcfSirP/zhD90zsA+2Q1fur6t9GuyCNwwNo7WlsJAY0wkZURmosAyUZpYTCSApIBQqgOc1j8JGgaLHk0qVqgLjBAz8RwHylQDvwRdoChLeFRUbEqLyQqq84oEDHiExOgapg0UqvChkh0x5y8AuFGIqLAl82fCysAdxNkiXe/CkmGxApSG+yFsIDQj2waYQVKrsQ1kCe8oMr968KSEL8oI1b1CUJWLreMRUbsiYEBavuNxDY8KbCvakgcfzT4V9fDFDJ5/AHzmRkT1vVtgN++Glgz0hPMiaOkUZxE6QEm8klMVUxKe9/OzRh7cosAdv3nxxqMCaukBZon4Qe+cNCjLGPtjE2wcbE1LgHvbgUlOZoxzHSg2WdFEYUHylBqRgYfLng8Bw/mL3BK9P5W/kDOrD32wkjgfPgYG/HhxSnbysXt6gPMgdq0Bzjnu8TSGmdEoeZ2TyegTlC+rr7RPUJ9o9wftT+dvLHpQ7eIzjbDT0/jh2jGXLVOhyMay93F42r6u3K3/Xtv7URLoNKrzgwfJ7b3T/dySoHsDg8Yvd45+V6j1yBuX2hd4XlOC5IDkFj6dKB497rPyR0evDNUGZ09k+QZwj5ebvoN5eJ/TEE/bJH/d/p8vey+7lQ+7IY5y7GAap1OdiWHt9kDGoZ1Anf7w+enxo7fo8JU3vvRhA0c5HO5aO6sWSM9rxaMdSqVNt5Yl2XbRjqdKFShyUJ/g7mkyxzsc6Hu0ZqToWTcbaHkuVzNHyjSazvy7auWjH/PV13af+XbOuktt9hkAKEcD7CXpAKRTFsg4ZAka6ITOYiZtaBPBuGalAZyA93fRgB19LUyud5R4GBIx0w2AlkzFtEMC7pScbwmU2HQRsHm/amCcUgjTomG4oLGBChgIBvFk6vBguxVAiYn0QriVD4FIRMNK9VMTs+oxCgHACiXHDzGpijCdjcAkrQML+fEaBYsrWCwEj3XrBZzdnAgLMXmQKMt/dYxA9n2/iGJNNjHQzoQTEV0eL6cYXT3taA0KAWC0z6Fj+j+m7TJ/+5je/6WYsMeuKQfNGug3I4ElSxTzdJAFt2YQPAeK4kCuLnrB+At9nY70HpoEypZSp5n52XPi0M4lThYB5uqlC3vJNewTwYlkzgSUZWRcBwqUDjbUEWI+D84kYPJ/2wJiA9ULASLde8NnNDR0BT6p0mhFu4G/I1gi3oVs+cfoZ6SYOW3tyyBEIerV4vMR3IV+O+2UxIV9LhsClIGCkeylo2bUZhQDxWuK3LNHIkpksgs2oBTrVWLAb8rXZaBlVJOKirHWkxQVGe0hDRADSZcFuvhRAp9m0adPcFyKI6ZIgXUuGwKUiYKR7qYjZ9RmDAKRK+ICRC3wSiE82MUmCv1n42sd5faghY4AxReuFgJFuveCzmxs6AkHi5SsQeL90qPmONMILNmysoZeC+OpX45cj4puVPc0QMAQMAUPAOtKsDBgChoAhkEQEjHSTCLZlZQgYAoaAka6VAUPAEDAEkoiAkW4SwbasDAFDwBAw0rUyYAgYAoZAEhEw0k0i2JaVIWAIGAJGulYGDAFDwBBIIgJGukkE27IyBAwBQ8BI18qAIWAIGAJJROD/A2mRTRQC1jEKAAAAAElFTkSuQmCC"></p>
<p style="text-align: left;">The NDCC want to find a model to predict the total number of people infected, so they can plan for medicine and hospital facilities. After looking at the data, they think an exponential function in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = a{b^d}">
  <mi>n</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mrow>
    <msup>
      <mi>b</mi>
      <mi>d</mi>
    </msup>
  </mrow>
</math></span> could be used as a model.</p>
</div>

<div class="specification">
<p>Use your answer to part (a) to predict</p>
</div>

<div class="specification">
<p>The NDCC want to verify the accuracy of these predictions. They decide to perform a <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ<!-- χ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> goodness of fit test.</p>
</div>

<div class="specification">
<p>The predictions given by the model for the first five days are shown in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>In fact, the first day when the total number of people infected is greater than 1000 is day 14, when a total of 1015 people are infected.</p>
</div>

<div class="specification">
<p>Based on this new data, the NDCC decide to try a logistic model in the form&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = \frac{L}{{1 + c{e^{ - kd}}}}">
  <mi>n</mi>
  <mo>=</mo>
  <mfrac>
    <mi>L</mi>
    <mrow>
      <mn>1</mn>
      <mo>+</mo>
      <mi>c</mi>
      <mrow>
        <msup>
          <mi>e</mi>
          <mrow>
            <mo>−<!-- − --></mo>
            <mi>k</mi>
            <mi>d</mi>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>.</p>
</div>

<div class="specification">
<p>Use the data from days 1–5, together with day 14, to find the value of</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use an exponential regression to find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>, correct to 4 decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the number of new people infected on day 6.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the day when the total number of people infected will be greater than 1000.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (a) to show that the model predicts 16.7 people will be infected on the first day.</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>Explain why the number of degrees of freedom is 2.</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>Perform a <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> goodness of fit test at the 5% significance level. You should clearly state your hypotheses, the p-value, and your conclusion.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Give two reasons why the prediction in part (b)(ii) might be lower than 14.</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 class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span>.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
  <mi>c</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence predict the total number of people infected by this disease after several months.</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 logistic model to find the day when the rate of increase of people infected is greatest.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A smartphone’s battery life is defined as the number of hours a fully charged battery can be used before the smartphone stops working. A company claims that the battery life of a model of smartphone is, on average, 9.5 hours. To test this claim, an experiment is conducted on a random sample of 20 smartphones of this model. For each smartphone, the battery life, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>&nbsp;hours, is measured and the sample mean, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar b}">
  <mrow>
    <mrow>
      <mover>
        <mi>b</mi>
        <mo stretchy="false">¯<!-- ¯ --></mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, calculated. It can be assumed the battery lives are normally distributed with standard deviation 0.4 hours.</p>
</div>

<div class="specification">
<p>It is then found that this model of smartphone has an average battery life of 9.8 hours.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State suitable hypotheses for a two-tailed test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the critical region for testing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar b}">
  <mrow>
    <mrow>
      <mover>
        <mi>b</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span> at the 5 % significance level.</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>Find the probability of making a Type II error.</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>Another model of smartphone whose battery life may be assumed to be normally distributed with mean <em>μ</em> hours and standard deviation 1.2 hours is tested. A researcher measures the battery life of six of these smartphones and calculates a confidence interval of [10.2, 11.4] for <em>μ</em>.</p>
<p>Calculate the confidence level of this interval.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>This question will connect Markov chains and directed graphs.</p>
<p>Abi is playing a game that involves a fair coin with heads on one side and tails on the other, together with two tokens, one with a fish’s head on it and one with a fish’s tail on it. She starts off with no tokens and wishes to win them both. On each turn she tosses the coin, if she gets a head she can claim the fish’s head token, provided that she does not have it already and if she gets a tail she can claim the fish’s tail token, provided she does not have it already. There are 4 states to describe the tokens in her possession; A: no tokens, B: only a fish’s head token, C: only a fish’s tail token, D: both tokens. So for example if she is in state B and tosses a tail she moves to state D, whereas if she tosses a head she remains in state B.</p>
</div>

<div class="specification">
<p>After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
  <mi>n</mi>
</math></span> throws the probability vector, for the 4 states, is given by&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\mathbf{v}}_n} = \left( {\begin{array}{*{20}{c}}  {{a_n}} \\   {{b_n}} \\   {{c_n}} \\   {{d_n}}  \end{array}} \right)">
  <mrow>
    <msub>
      <mrow>
        <mrow>
          <mi mathvariant="bold">v</mi>
        </mrow>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
  <mo>=</mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mrow>
              <mrow>
                <msub>
                  <mi>a</mi>
                  <mi>n</mi>
                </msub>
              </mrow>
            </mrow>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mrow>
              <mrow>
                <msub>
                  <mi>b</mi>
                  <mi>n</mi>
                </msub>
              </mrow>
            </mrow>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mrow>
              <mrow>
                <msub>
                  <mi>c</mi>
                  <mi>n</mi>
                </msub>
              </mrow>
            </mrow>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mrow>
              <mrow>
                <msub>
                  <mi>d</mi>
                  <mi>n</mi>
                </msub>
              </mrow>
            </mrow>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span> where the numbers represent the probability of being in that particular state, e.g.&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{b_n}">
  <mrow>
    <msub>
      <mi>b</mi>
      <mi>n</mi>
    </msub>
  </mrow>
</math></span>&nbsp;is the probability of being in state B after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
  <mi>n</mi>
</math></span>&nbsp;throws. Initially&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\mathbf{v}}_0} = \left( {\begin{array}{*{20}{c}}  1 \\   0 \\   0 \\   0  \end{array}} \right)">
  <mrow>
    <msub>
      <mrow>
        <mrow>
          <mi mathvariant="bold">v</mi>
        </mrow>
      </mrow>
      <mn>0</mn>
    </msub>
  </mrow>
  <mo>=</mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mn>1</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>0</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>0</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>0</mn>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a transition state diagram for this Markov chain problem.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why for any transition state diagram the sum of the out degrees of the directed edges from a vertex (state) must add up to +1.</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>Write down the transition matrix <strong>M</strong>, for this Markov chain problem.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the steady state probability vector for this Markov chain problem.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain which part of the transition state diagram confirms this.</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>Explain why having a steady state probability vector means that the matrix <strong>M</strong> must have an eigenvalue of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda  = 1"> <mi>λ</mi> <mo>=</mo> <mn>1</mn> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\mathbf{v}}_1}{\text{,}}\,\,{{\mathbf{v}}_2}{\text{,}}\,\,{{\mathbf{v}}_3}{\text{,}}\,\,{{\mathbf{v}}_4}\,"> <mrow> <msub> <mrow> <mrow> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mn>1</mn> </msub> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <msub> <mrow> <mrow> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mn>2</mn> </msub> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <msub> <mrow> <mrow> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mn>3</mn> </msub> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <msub> <mrow> <mrow> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mn>4</mn> </msub> </mrow> <mspace width="thinmathspace"></mspace> </math></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>Hence, deduce the form of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\mathbf{v}}_n}"> <mrow> <msub> <mrow> <mrow> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mi>n</mi> </msub> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain how your answer to part (f) fits with your answer to part (c).</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the minimum number of tosses of the coin that Abi will have to make to be at least 95% certain of having finished the game by reaching state C.</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question explores models for the height of water in a cylindrical container as&nbsp;water drains out.</strong></p>
<p><br>The diagram shows a cylindrical water container of height <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>2</mn></math> metres and base radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> metre.&nbsp;At the base of the container is a small circular valve, which enables water to drain out.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Eva closes the valve and fills the container with water.</p>
<p style="text-align: left;">At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, Eva opens the valve. She records the height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres, of water remaining in&nbsp;the container every <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> minutes.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Eva first tries to model the height using a linear function, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mi>t</mi><mo>+</mo><mi>b</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#8712;</mo><mi mathvariant="normal">&#8477;</mi></math>.</p>
</div>

<div class="specification">
<p>Eva uses the equation of the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, to predict the time it will take for all&nbsp;the water to drain out of the container.</p>
</div>

<div class="specification">
<p>Eva thinks she can improve her model by using a quadratic function, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>p</mi><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mi>q</mi><mi>t</mi><mo>+</mo><mi>r</mi></math>,&nbsp;where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mo>&#160;</mo><mi>q</mi><mo>,</mo><mo>&#160;</mo><mi>r</mi><mo>&#8712;</mo><mi mathvariant="normal">&#8477;</mi></math>.</p>
</div>

<div class="specification">
<p>Eva uses this equation to predict the time it will take for all the water to drain out of the&nbsp;container and obtains an answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> minutes.</p>
</div>

<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume, in cubic metres, of water in the container at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>&nbsp;minutes.<br>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the radius, in metres, of the circular valve.</p>
<p>Eva does some research and discovers a formula for the rate of change of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mo>-</mo><mi>&#960;</mi><msup><mi>R</mi><mn>2</mn></msup><msqrt><mn>70</mn><mo>&#8202;</mo><mn>560</mn><mi>h</mi></msqrt></math></p>
</div>

<div class="specification">
<p>Eva measures the radius of the valve to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>023</mn></math> metres. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> be the time, in minutes,&nbsp;it takes for all the water to drain out of the container.</p>
</div>

<div class="specification">
<p>Eva wants to use the container as a timer. She adjusts the initial height of water in the&nbsp;container so that all the water will drain out of the container in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> minutes.</p>
</div>

<div class="specification">
<p>Eva has another water container that is identical to the first one. She places one water container above the other one, so that all the water from the highest container will drain into the lowest container. Eva completely fills the highest container, but only fills the lowest container to a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> metre, as shown in the diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> Eva opens both valves. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> be the height of water, in metres, in the lowest container at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret the meaning of parameter <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> in the context of the model.</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>Suggest why Eva’s use of the linear regression equation in this way could be unreliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the least squares quadratic regression curve.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</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>Hence, write down a suitable domain for Eva’s function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>p</mi><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mi>q</mi><mi>t</mi><mo>+</mo><mi>r</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>h</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mo>-</mo><msup><mi>R</mi><mn>2</mn></msup><msqrt><mn>70</mn><mo> </mo><mn>560</mn><mi>h</mi></msqrt></math>.</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>By solving the differential equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>h</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mo>-</mo><msup><mi>R</mi><mn>2</mn></msup><msqrt><mn>70</mn><mo> </mo><mn>560</mn><mi>h</mi></msqrt></math>, show that the general solution is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>17</mn><mo> </mo><mn>640</mn><msup><mfenced><mrow><mi>c</mi><mo>-</mo><msup><mi>R</mi><mn>2</mn></msup><mi>t</mi></mrow></mfenced><mn>2</mn></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the general solution from part (d) and the initial condition <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>2</mn></math> to predict the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</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>Find this new height.</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>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>H</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>≈</mo><mn>0</mn><mo>.</mo><mn>2514</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>009873</mn><mi>t</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>1405</mn><msqrt><mi>H</mi></msqrt></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mi>T</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Euler’s method with a step length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn></math> minutes to estimate the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question uses statistical tests to investigate whether advertising leads to increased profits for a grocery store.</strong></p>
<p><br>Aimmika is the manager of a grocery store in Nong Khai. She is carrying out a statistical analysis on the number of bags of rice that are sold in the store each day. She collects the following sample data by recording how many bags of rice the store sells each day over a period of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math> days.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>She believes that her data follows a Poisson distribution.</p>
</div>

<div class="specification">
<p>Aimmika knows from her historic sales records that the store sells an average of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>2</mn></math> bags of rice each day. The following table shows the expected frequency of bags of rice sold each day during the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math> day period, assuming a Poisson distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>2</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>Aimmika decides to carry out a <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>&#967;</mi><mn>2</mn></msup></math> goodness of fit test at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level to see&nbsp;whether the data follows a Poisson distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>2</mn></math>.</p>
</div>

<div class="specification">
<p>Aimmika claims that advertising in a local newspaper for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math> Thai Baht <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(THB)</mtext></math> per day&nbsp;will increase the number of bags of rice sold. However, Nichakarn, the owner of the store,&nbsp;claims that the advertising will <strong>not</strong> increase the store&rsquo;s overall profit.</p>
<p>Nichakarn agrees to advertise in the newspaper for the next <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> days. During that time,&nbsp;Aimmika records that the store sells <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>282</mn></math> bags of rice with a profit of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>495</mn><mo>&#8202;</mo><mtext>THB</mtext></math> on&nbsp;each bag sold.</p>
</div>

<div class="specification">
<p>Aimmika wants to carry out an appropriate hypothesis test to determine whether the&nbsp;number of bags of rice sold during the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> days increased when compared with the&nbsp;historic sales records.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean and variance for the sample data given in the table.</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>Hence state why Aimmika believes her data follows a Poisson distribution.</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>State one assumption that Aimmika needs to make about the sales of bags of rice to support her belief that it follows a Poisson distribution.</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 value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>, and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>. Give your answers to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> decimal places.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for her test.</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>Perform the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> goodness of fit test and state, with reason, a conclusion.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By finding a critical value, perform this test at a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mo>%</mo></math> significance level.</p>
<div class="marks">[6]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence state the probability of a Type I error for this test.</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>By considering the claims of both Aimmika and Nichakarn, explain whether the advertising was beneficial to the store.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><em>This question explores methods to analyse the scores in an exam.</em></p>
<p>A random sample of 149 scores for a university exam are given in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The university wants to know if the scores follow a normal distribution, with the mean and variance found in part (a).</p>
</div>

<div class="specification">
<p>The expected frequencies are given in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The university assigns a pass grade to students whose scores are in the top 80%.</p>
</div>

<div class="specification">
<p>The university also wants to know if the exam is gender neutral. They obtain random samples of scores for male and female students. The mean, sample variance and sample size are shown in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The university awards a distinction to students who achieve high scores in the exam. Typically, 15% of students achieve a distinction. A new exam is trialed with a random selection of students on the course. 5 out of 20 students achieve a distinction.</p>
</div>

<div class="specification">
<p>A different exam is trialed with 16 students. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span> be the percentage of students achieving a distinction. It is desired to test the hypotheses</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_0}\,{\text{:}}\,p = 0.15">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>0</mn>
    </msub>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>:</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>p</mi>
  <mo>=</mo>
  <mn>0.15</mn>
</math></span> against&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_1}\,{\text{:}}\,p > 0.15">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>1</mn>
    </msub>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>:</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>p</mi>
  <mo>&gt;</mo>
  <mn>0.15</mn>
</math></span></p>
<p>It is decided to reject the null hypothesis if the number of students achieving a distinction is greater than 3.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find unbiased estimates for the population mean.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find unbiased estimates for the population Variance.</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>Show that the expected frequency for 20 &lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> ≤ 4 is 31.5 correct to 1 decimal place.</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>Perform a suitable test, at the 5% significance level, to determine if the scores follow a normal distribution, with the mean and variance found in part (a). You should clearly state your hypotheses, the degrees of freedom, the<em> p</em>-value and your conclusion.</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the normal distribution model to find the score required to pass.</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>Perform a suitable test, at the 5% significance level, to determine if there is a difference between the mean scores of males and females. You should clearly state your hypotheses, the<em> p</em>-value and your conclusion.</p>
<div class="marks">[6]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Perform a suitable test, at the 5% significance level, to determine if it is easier to achieve a distinction on the new exam. You should clearly state your hypotheses, the critical region and your conclusion.</p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of making a Type I error.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.2">
  <mi>p</mi>
  <mo>=</mo>
  <mn>0.2</mn>
</math></span> find the probability of making a Type II error.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Juliet is a sociologist who wants to investigate if income affects happiness amongst&nbsp;doctors. This question asks you to review Juliet’s methods and conclusions.</strong></p>
<p>Juliet obtained a list of email addresses of doctors who work in her city. She contacted them&nbsp;and asked them to fill in an anonymous questionnaire. Participants were asked to state their&nbsp;annual income and to respond to a set of questions. The responses were used to determine&nbsp;<em>a happiness score</em> out of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math>. Of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>415</mn></math> doctors on the list, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math> replied.</p>
</div>

<div class="specification">
<p>Juliet’s results are summarized in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>For the remaining ten responses in the table, Juliet calculates the mean happiness&nbsp;score to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn><mo>.</mo><mn>5</mn></math>.</p>
</div>

<div class="specification">
<p>Juliet decides to carry out a hypothesis test on the correlation coefficient to investigate&nbsp;whether increased annual income is associated with greater happiness.</p>
</div>

<div class="specification">
<p>Juliet wants to create a model to predict how changing annual income might affect&nbsp;happiness scores. To do this, she assumes that annual income in dollars, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>, is the&nbsp;independent variable and the happiness score, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math>, is the dependent variable.</p>
<p>She first considers a linear model of the form</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mi>a</mi><mi>X</mi><mo>+</mo><mi>b</mi></math>.</p>
</div>

<div class="specification">
<p>Juliet then considers a quadratic model of the form</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mi>c</mi><msup><mi>X</mi><mn>2</mn></msup><mo>+</mo><mi>d</mi><mi>X</mi><mo>+</mo><mi>e</mi></math>.</p>
</div>

<div class="specification">
<p>After presenting the results of her investigation, a colleague questions whether Juliet’s&nbsp;sample is representative of all doctors in the city.</p>
<p>A report states that the mean annual income of doctors in the city is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>80</mn><mo> </mo><mn>000</mn></math>. Juliet&nbsp;decides to carry out a test to determine whether her sample could realistically be&nbsp;taken from a population with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>80</mn><mo> </mo><mn>000</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe <strong>one</strong> way in which Juliet could improve the reliability of her investigation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe <strong>one</strong> criticism that can be made about the validity of Juliet’s investigation.</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>Juliet classifies response <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>K</mtext></math> as an outlier and removes it from the data. Suggest <strong>one&nbsp;</strong>possible justification for her decision to remove it.</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>Calculate the mean <strong>annual income</strong> for these remaining responses.</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>Determine the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, Pearson’s product-moment correlation coefficient,&nbsp;for these remaining responses.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why the hypothesis test should be one-tailed.</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>State the null and alternative hypotheses for this test.</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>The critical value for this test, at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>549</mn></math>. Juliet assumes that&nbsp;the population is bivariate normal.</p>
<p>Determine whether there is significant evidence of a positive correlation between&nbsp;annual income and happiness. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Juliet’s data to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret, referring to income and happiness, what the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> represents.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>, of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coefficient of determination for each of the two models she considers.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence compare the two models.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.v.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Juliet decides to use the coefficient of determination to choose between these&nbsp;two models.</p>
<p>Comment on the validity of her decision.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.vi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name of the test which Juliet should use.</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>State the null and alternative hypotheses for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Perform the test, using a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level, and state your conclusion&nbsp;in context.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> has a distribution with mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ<!-- μ --></mi>
</math></span> and variance 4. A random sample of&nbsp;size 100 is to be taken from the distribution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>Josie takes a different random sample of size 100 to test the null hypothesis that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu&nbsp; = 60">
  <mi>μ<!-- μ --></mi>
  <mo>=</mo>
  <mn>60</mn>
</math></span>&nbsp;against the alternative hypothesis that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu&nbsp; > 60">
  <mi>μ<!-- μ --></mi>
  <mo>&gt;</mo>
  <mn>60</mn>
</math></span> at the 5 % level.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the central limit theorem as applied to a random sample of size <span class="mjpage"><math alttext="n" xmlns="http://www.w3.org/1998/Math/MathML"> <mi>n</mi> </math></span>, taken from a&nbsp;distribution with mean <span class="mjpage"><math alttext="\mu " xmlns="http://www.w3.org/1998/Math/MathML"> <mi>μ</mi> </math></span> and variance <span class="mjpage"><math alttext="{\sigma ^2}" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Jack takes a random sample of size 100 and calculates that <span class="mjpage"><math alttext="\bar x = 60.2" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> <mo>=</mo> <mn>60.2</mn> </math></span>. Find an&nbsp;approximate 90 % confidence interval for <span class="mjpage"><math alttext="\mu " xmlns="http://www.w3.org/1998/Math/MathML"> <mi>μ</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the critical region for Josie’s test, giving your answer correct to two decimal&nbsp;places.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that Josie makes a Type I error.</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>Given that the probability that Josie makes a Type II error is 0.25, find the value&nbsp;of <span class="mjpage"><math alttext="\mu " xmlns="http://www.w3.org/1998/Math/MathML"> <mi>μ</mi> </math></span>, giving your answer correct to three significant figures.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>A firm wishes to review its recruitment processes. This question considers the validity&nbsp;and reliability of the methods used.</strong></p>
<p>Every year an accountancy firm recruits new employees for a trial period of one year from a&nbsp;large group of applicants.</p>
<p>At the start, all applicants are interviewed and given a rating. Those with a rating of either&nbsp;<em>Excellent</em>, <em>Very good</em> or <em>Good</em> are recruited for the trial period. At the end of this period,&nbsp;some of the new employees will stay with the firm.</p>
<p>It is decided to test how valid the interview rating is as a way of predicting which of the new&nbsp;employees will stay with the firm.</p>
<p>Data is collected and recorded in a contingency table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The next year’s group of applicants are asked to complete a written assessment which&nbsp;is then analysed. From those recruited as new employees, a random sample of size <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math>&nbsp;is selected.</p>
<p>The sample is stratified by department. Of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>91</mn></math> new employees recruited that year,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math> were placed in the national department and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math> in the international department.</p>
</div>

<div class="specification">
<p>At the end of their first year, the level of performance of each of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> employees in the&nbsp;sample is assessed by their department manager. They are awarded a score between&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> (low performance) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> (high performance).</p>
<p>The marks in the written assessment and the scores given by the managers are shown in&nbsp;both the table and the scatter diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The firm decides to find a Spearman’s rank correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>, for this data.</p>
</div>

<div class="specification">
<p>The same seven employees are given the written assessment a second time, at the end of&nbsp;the first year, to measure its reliability. Their marks are shown in the table below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The written assessment is in five sections, numbered <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math>. At the end of the year,&nbsp;the employees are also given a score for each of five professional attributes:&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext><mo>,</mo><mo>&nbsp;</mo><mtext>W</mtext><mo>,</mo><mo>&nbsp;</mo><mtext>X</mtext><mo>,</mo><mo>&nbsp;</mo><mtext>Y</mtext></math>&nbsp;and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math>.</p>
<p>The firm decides to test the hypothesis that there is a correlation between the mark&nbsp;in a section and the score for an attribute.</p>
<p>They compare marks in <strong>each</strong> of the sections with scores for <strong>each</strong> of the attributes.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use an appropriate test, at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level, to determine whether a new&nbsp;employee staying with the firm is independent of their interview rating. State the null&nbsp;and alternative hypotheses, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value and the conclusion of the test.</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>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math> employees are selected for the sample from the national department.</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>Without calculation, explain why it might not be appropriate to calculate a&nbsp;correlation coefficient for the whole sample of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> employees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math> for the seven employees working in the <strong>international</strong> department.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence comment on the validity of the written assessment as a measure of the&nbsp;level of performance of employees in this department. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name of this type of test for reliability.</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 the data in this table, test the null hypothesis, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub><mo>:</mo><mi>ρ</mi><mo>=</mo><mn>0</mn></math>, against the&nbsp;alternative hypothesis, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>1</mn></msub><mo>:</mo><mi>ρ</mi><mo>&gt;</mo><mn>0</mn></math>, at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level. You may&nbsp;assume that all the requirements for carrying out the test have been met.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence comment on the reliability of the written assessment.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of tests they carry out.</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>The tests are performed at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level.<br><br>Assuming that:</p>
<ul>
<li>there is no correlation between the marks in any of the sections and scores&nbsp;in any of the attributes,</li>
<li>the outcome of each hypothesis test is independent of the outcome of the&nbsp;other hypothesis tests,</li>
</ul>
<p>find the probability that at least one of the tests will be significant.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The firm obtains a significant result when comparing section <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> of the written&nbsp;assessment and attribute <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>. Interpret this result.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The random variables <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="U,{\text{ }}V">
  <mi>U</mi>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mi>V</mi>
</math></span> follow a bivariate normal distribution with product moment correlation coefficient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho ">
  <mi>ρ<!-- ρ --></mi>
</math></span>.</p>
</div>

<div class="specification">
<p>A random sample of 12 observations on&nbsp;<em>U</em>, <em>V</em> is obtained to determine whether there is a correlation between <em>U and</em>&nbsp;<em>V</em>. The sample product moment correlation coefficient is denoted by <em>r</em>. A test to determine whether or not <em>U</em>,&nbsp;<em>V</em> are independent is carried out at the 1% level of significance.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State suitable hypotheses to investigate whether or not <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="U">
  <mi>U</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V">
  <mi>V</mi>
</math></span> are independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="|r|">
  <mrow>
    <mo stretchy="false">|</mo>
  </mrow>
  <mi>r</mi>
  <mrow>
    <mo stretchy="false">|</mo>
  </mrow>
</math></span> for which the test concludes that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho&nbsp; \ne 0">
  <mi>ρ</mi>
  <mo>≠</mo>
  <mn>0</mn>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer sells bags of potatoes which he states have a mean weight of 7 kg . An inspector, however, claims that the mean weight is less than 7 kg . In order to test this claim, the inspector takes a random sample of 12 of these bags and determines the weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> kg , of each bag. He finds that <span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\sum {x = 83.64;{\text{ }}\sum {{x^2} = 583.05.} } ">
  <mo>∑<!-- ∑ --></mo>
  <mrow>
    <mi>x</mi>
    <mo>=</mo>
    <mn>83.64</mn>
    <mo>;</mo>
    <mrow>
      <mtext>&nbsp;</mtext>
    </mrow>
    <mo>∑<!-- ∑ --></mo>
    <mrow>
      <mrow>
        <msup>
          <mi>x</mi>
          <mn>2</mn>
        </msup>
      </mrow>
      <mo>=</mo>
      <mn>583.05.</mn>
    </mrow>
  </mrow>
</math></span> You may assume that the weights of the bags of potatoes can be modelled by the normal distribution <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{N}}(\mu ,{\text{ }}{\sigma ^2})">
  <mrow>
    <mtext>N</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>μ<!-- μ --></mi>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msup>
      <mi>σ<!-- σ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State suitable hypotheses to test the inspector’s claim.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find unbiased estimates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2}">
  <mrow>
    <msup>
      <mi>σ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Carry out an appropriate test and state the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>-value obtained.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using a 10% significance level and justifying your answer, state your conclusion in context.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two IB schools, A and B, follow the IB Diploma Programme but have different teaching methods.&nbsp;A research group tested whether the different teaching methods lead to a similar final result.</p>
<p>For the test, a group of eight students were randomly selected from each school. Both samples&nbsp;were given a standardized test at the start of the course and a prediction for total IB points was&nbsp;made based on that test; this was then compared to their points total at the end of the course.</p>
<p>Previous results indicate that both the predictions from the standardized tests and the final&nbsp;IB points can be modelled by a normal distribution.</p>
<p>It can be assumed that:</p>
<ul>
<li>the standardized test is a valid method for predicting the final IB points</li>
<li>that variations from the prediction can be explained through the circumstances of&nbsp;the student or school.</li>
</ul>
</div>

<div class="specification">
<p>The data for school A is shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoYAAAGICAYAAADcaCGUAAAgAElEQVR4Aey9C3RT55nv/becoTQ1lzIwgwQpDLg2ZHCSYh/TJLTIdpGbSSHUBGhJbBH7JHAaCCdeYAXn0jbhEmMvMyShhXKsGEiYQrDGNJNJbWLFyUAprkyT4lOwCnzQYok5SSnYSgIk3vtbe0tb2pIlWZblm/z3WqCtvd/3eZ/n996e/d6UIIqiCP6RAAmQAAmQAAmQAAkMewKaYU+AAEiABEiABEiABEiABGQCdAxZEEiABEiABEiABEiABGQCdAxZEEiABEiABEiABEiABGQCdAxZEEiABAaYwE04my2oMKYhISHB8y8XJrMVdpfQQ92+gNOyyi3DaIGzh7F7F/wvsBiTkZCQDKPlL5GLEs7AnJuMXPMZ9NTayBNhSBIgARKIjAAdw8g4MRQJkECfELgJp3ULlmcsxvq9LaoU6rG1KAepC7ajucfOoUrMELgUzv4GB+rPof7Ab3CWnuEQyDGqSALxTYCOYXznL60jgcFNQDiPt8t2oRGAtqAapzs6IYo34Gj4CfSS5o3lKD1oj+ORtKv4/a8sqJdsrbfgV7+/Orjzi9qRAAnEPQE6hnGfxTSQBAYxAeETXDnnnvC9NW0WkpOkJmkEtPplyDdoAThxqtUBl9eErtPOOuM2HLG3e0OoLwRnE/aYct1Ty1km7Gl2BjiZ7bBbD6imsXXIMplh7SJPgMveiEMVRuiU6e4sE8xWu0o3dcoRXrefRM2RT3CPHPwtVB48ieCWRCiPwUiABEigtwSkcwz5RwIkQAIDQqDztFhl0EpnqYqAQSypqhEbWq+FUKVT7LBVino5rBRe9U/7uFhz6YYoip+LjpqV7mf65WKBXpGthF0iVrV+5pF/TTxdVShq1XK81/eL5ba/ecJ1ih2nq8UCrSJD/akV9eUnxA455J/FmoLpIjBdLKj5cwgb1LdviJdqNogb6t/1MdBuEBuudaoD8ZoESIAE+pUARwx761kzPgmQQPQENClYun0LCqTBQUjrChcjJ3UMEhLSYKzYj8PqET7BjoOl5WiEFvoN9XB0ihA7L6FhgwFw7sDql476j7Y1foyJa6zoEEV0OuqxQS8lchLvtXwk6yvYD2FtkRlOzEJB1Sk5nFce3sL6da+61zdK6a7dgL3OYNPdTjSufx47m6OYAhbOo858C74z55vIXZkHGYGzGmWH4nnqPPqiwpgkQAL9Q4COYf9wZiokQAJBCWiQNMOIV5ttqK0qca8rlMO1YO/6h7Aow4BHzC3u6dr//iPeq5emnRdizZosaKXWSzMJ2ZvrIP2Ak6MsG6PVaRiWoWjRDCRJwbTfwHcydaqn13H26K/da/sMT+LpFbPkcLK8p0wokby0xl/h3dZP4d4cIqW7BBufXoYZynR39uN4tiQdwFvY+e45fKGSHsmlcPYEjum/h8zRIzHpO3nId3uG3IQSCTyGIQES6DMCdAz7DC0FkwAJREpAo03HA4VleFcUIXa0oqHmFyiRR/hasPeZ/WhqF/CF4zyORSpQCjdxLEZ5W7iRGDNhlCr2F+i44h45nD7/TkzzhgNw6xhMuFUK+hecuvg3CB1XcE76Oj0Td04bqZLhk3nu1EW4pakeh738GI1Vx3HvwjvcDunoO5CbLzmZ3IQSFhsfkgAJ9DkBdXPY54kxARIgARLwERDQbi31bOZYCrP9uvtRUgqy8x7FpopiTJfuOI/j5J8+xS26abhXDnEFVzt6Oj7nS9V9dQtGjZsgX5478iHOq4+J+fQaPvpUenQb0qZ8FZpR49x6nGvCh+c9Osoxr+PaRx3y1fS0KXBLk792/1/7H1C3bxeKUr/sObdxAnK2NnvicRNK9wAZggRIoK8I0DHsK7KUSwIk0A0BDUZnfMczhfoGntlUhSbnTXccVwv2vrTHPVKnvRuzv34r8I+3Y568U/ko9lX/F5yyM9eOM+Yit3OZa4Zd7eCFTX0kkud+FwYpTP02bKr2TFcLbbC+WIat0syxfiGyUm+FJvkeLJPTlXQ8gDPyuYrS+Ys78ILszN2PVVnTcUvY9NQPb6LtnXeQ+NpH8hS4NA0u/+s8jSo5HcC57x3Y2iM2Ri2c1yRAAiTQOwL9utWFiZEACZCAHwFpZ+7jIXYGS7t/Z4kFVac8u37D7EqGQdzQcEnsVO9KLqgRHd60OkRbuT5gx/DfRFv5/f67m0PtSg61Gxo93ZV8Q3Q0/ETUB9197M9CW1Atnu7gDmVvFvKCBEigXwhwxLB3fjVjkwAJ9IrACEzKq0Sz7U1Ulcjjd15p2oJyvNFQgx2Fno0h0CAp/XHst9WgvGCWX7gaWzU2Zk9Czxq0sUhftx+tDb9UydNCX1KFhtb9WJc+1pOGlO5avNn6Lt4oL3DvHpae6EtQ1dCIN9dlutcJejUKdeFCc0UudDk/QaNzC3LGpKh+Os/9bPLiHd6f8XPuXYGZo34Ei7O30+ah9OF9EiABEuhKIEFyP7ve5h0SIAESIAESIAESIIHhRqBnL9jDjQ7tJQESIAESIAESIIFhRICO4TDKbJpKAiRAAiRAAiRAAuEI0DEMR4fPSIAESIAESIAESGAYEaBjOIwym6aSAAmQAAmQAAmQQDgCdAzD0eEzEiABEiABEiABEhhGBOgYDqPMpqkkQAIkQAIkQAIkEI4AHcNwdPiMBEiABEiABEiABIYRATqGwyizaSoJkAAJkAAJkAAJhCNAxzAcHT4jARIgARIgARIggWFEgI7hMMpsmkoCJEACJEACJEAC4QjQMQxHh89IgARIgARIgARIYBgRoGM4jDKbppIACZAACZAACZBAOAJ0DMPR4TMSIAESIAESIAESGEYE6BgOo8ymqSRAAiRAAiRAAiQQjgAdw3B0+IwESIAESIAESIAEhhEBOobDKLNpKgmQAAmQAAmQAAmEI0DHMBwdPiMBEiABEiABEiCBYUSAjuEwymyaSgIkQAIkQAIkQALhCNAxDEeHz0iABEiABEiABEhgGBGgYziMMpumkgAJkAAJkAAJkEA4AnQMw9HhMxIgARIgARIgARIYRgToGA6jzKapJEACJEACJEACJBCOAB3DcHT4jARIgARIgARIgASGEQE6hsMos2kqCZAACZAACZAACYQjQMcwHB0+IwESIAESIAESIIFhROCW7mxNSEjoLgifkwAJkAAJkAAJkAAJDEECoij6ad2tYyiFDozkJ4FfSGCACUgvLyyjfZMJZNs3XCk1/gmw7sR/Hg91C0OVUU4lD/Wcpf4kQAIkQAIkQAIkECMCdAxjBJJiSIAESIAESIAESGCoE6BjONRzkPqTAAmQAAmQAAmQQIwI0DGMEUiKIQESIAESIAESIIGhToCO4VDPQepPAiRAAiRAAiRAAjEiQMcwRiAphgRIgARIgARIgASGOgE6hkM9B6k/CZAACZAACZAACcSIAB3DGIGkGBIgARIgARIgARIY6gToGA71HKT+JEACJEACJEACJBAjAnQMYwSSYkiABEiABEiABEhgqBMYQMfwJpzNFlQY0yD9LIv7Xy5MZivsLkHFVYDL3ohDFSZsa3ap7vfu8ovmCiRL6SZXoPmL3skKHrtv9A6eVqzuutBckeXOC6MFzliJHQpyBCeaD++GKUunKo86ZJl243CzE+oS2S/mfNGMimSpXmShIoblvl90lxNRlSVv/VbqeRqMFRY0O2/2rTpdGH4Bp2VVlOW7HXbrAVSs2hGj9sLHJ7miGcGboL/AYkyW9fWG8dqksFR/SuV1X99z7ZJrip7JMFr+0uVptzdcdlgPVWDVtlAcupUQEECAq3kbshJ0yDWf6WHdvQ67eSkSEr6HiuarAXL7+quvTPj6RHX+Knx7U44jsSFC+U4LjHLd9rVR3n61S52X7MiFaU8TnP3dmHr1XAWLM3hNC02lL/rxq2iu+B4SEpbCbL8eOmn1E5cdRyqM0Mlc01Bkuegu18IZmHN1SMjahmY/v0kduefXA+QY3oTTugXLMxZj/d4Wldb12FqUg9QF231GfvF77PyXLCxZ34ROVchBfzlU9R70YGOvoOA8gtKcdGQsegxbG9XusBONWx/DogwDHjG3IHavJbG3YWhJbMHe9YuRsXyHr54PcgO+aP4F/iXnB1j/zmeDWFOpvBYMKa6AC807VyJnyXq8E6sGXrDjYGk5GrUrYHowBT3r5EYi5cFVKNG+hfWlFtj724kZxKWr96rVY+uKRVhe2TR02tI+6McFuwWl69+CtmQVHkwZ2S1WuX9aoIfhrUl4pfUsGkpG4/z5/8anUkxNCh40rYC2sRylB+09fAkKnXTP6kxoOT17IpzH22W70AhAW1CN0x2dEMUbcDT8BHpJUoyN7JlyDD2sCAgXUftMMbZIDqG+BNU2BzpFEaLYiY7WGpTotQBasPeZnahv6+MRrrgEPx0FNX+GKDOVuN6A48QrKJCwNr6Og01X+tHqW6DN2+nWZU8eJBWG7t9K1Dg+V3EV0XmpBoUDwvU25O05C1E8iz15tw0wUgHtjXvxTL0T2vzvIGN0FF3c6DuQm58O1P8MVY0fD4g908tt+NxbZ6R6I/1T+A6BclxQA4ef/jdwqeZxaOFEY2Utmtr70ePW5mGPrMtO5GlvGZD89CX6MRqrfoZ6pCM/9w6M9j0IfuXtn2ajvKIEeSnTkV12DO+uy0SSHEOD0RnfQb7Wifpn9qIxRlyjqDXB9e/RXeETXDnnHpm5NW0WkpMkNUZAq1+GfIPUsjlxqtUBlzQE/HcZWH9Okt6I9RmjPFO/oYa6laF4Zcjdo1XAMKyxog72a8GGlKXpIrNqOjFwalud7n40q6fCdUZsa/JMOYbUOwgl1TD3oebfwqIaLjZuO6Yadg8xXeOdWlKGyRUGCUiuOII/HtkGo04axpemmSywu76Ay17nm8LPMmFP0KnS63A07fDETYDOuA1H7O3+BkhTQGYTspRpgywTzFa76m1Q0TkLL1oOoVSepo1mesc/2dh9kzqRXVhtbgG0j6PmtRdgTNd6Rhg0SErJw5ZdW1BY8gvUvPYEDJNGeJKWphesMJtyPdPOElszrGo+EeerJLIddm8+KayDOUw9SDf5p7DU/dSTNz2Ysogd3BCSRkCbuRAPzJ8O4CouX5VG4LopJ92Ws0gZquuveqlE12UtvvLujvN3GeshN0Pn1iPj76S6pUx7dtdmSLpJ+aaqczojKo604loIQtHe1kz6H7jfj2sISd6yWQSz9T98bUHQqT5lKk2ZxkpAQsh6rm53lTxNhvHQb9FsqVC1JTvQJC8jkMLchYz10hABcG59Bv7Ou3QikGuwdIPZdwW2uno4MR3z53y9+443mAiMxcw5GQCasa/uDwho9YLG6N+bwcpxJLwVLf3bG2naWmesgCVoP6DE6e3nCEy6OxvzJTHOK7j6SSjHUG3bblhV7aJU7rr2VZ4lHt4laeHbYu9UsrcOrELIflcKE9T/ABDYJsn9a0AfEAxZ+x9Qt68ZQAbmzBwbLITq3k201ZbL/ZO2sBA//EaI8KO/jjlSvXfWo84WrN9QiYz0UuzmD5BeVmL813larDJoRUk2YBBLqmrEhtZrXRNx1IgFchgpnOff9HLR9vnnoqNmpfteQY3o8MbsEG3lehGYLhbU/Nl9t/OCWFM4yxdfkaN8yvKkoDfESzWPi1rlvupTW1Atnu7oFEVRla7quVc3LBGrWj8TxZB6exX1XQQL65WtFQ1Vp0UpZVH8s1hTMN3fNun25zaxfLrEZqVY4/hcFEWFgYqZSp6+uFgs0AY8024QG65JqYSLCxHaQrHqtCefQnKdJRZUnRI7/HRWp5culjR8JD+N1X/Rl1GfvdqSBjFICQyqYuelGrEwkKHEWM0n4nwNXe7c5UovltvcNKNO15u/Qc0Je7P3bFV1UU7phug48YqnDCq2KWU7SDmJqJxFylBVf73tRqfYYasU9d46otJB+7hYc+kTX1ujCjO93CZ+HlGbIYoh880jzy0rWDb4uHjDdKnvSrxOseN0tZurrPcN5UHXz27Kpr78hKf+qmSqbHeXS63oC6foqc5r5Z6Kp1qGoUps7QwWRioT10LnCe4Xy21/62qTcudag1gi101PW6zcVz47WsWGmtfF8gKDWFLzvthQVeLOe3XdFUWxs7VKNEj69mvd8bVH3vxW9Pb7DFaOg7FUsZd5S0LC1BVvuQkm308B9xdvOVLqsdQdlYvTJW7e+qXEuyaeriqU+1dtYY14yd2pKQ9Vn6q01eXFe63Of59Md5lU2asuJ149lT5SDN5He9Pw9LveeCq5sr/wN9FWfn9wn0JfKdpkX0FlkveyU7zWsMHtY3jzw/vQ/8LPR3KnH7qP+kxsrVoi6xM6jL945Vuo9r1bry9UREVwdJ+hGpxZYkH562KtzeFxhtSOj6/w+TlofgVQqVhKA6XKCBjEDQ2XZLmdjqNiZYHHWVQcQ6VBUTcQHafEKjmc4syoC63UsJyWG1Bfw6+kG0rvILS8hU8r6ktqxFapUKk7Q699SsVXpSGJ69JRKAzUjoq6ICuOm7pDVNiq4vrxqhc36N2OvLvg+bj6nGZVnnobU0VniFAqTOcnYscnIVuFIIC6vxV9GVX0Uzvg3aX3kdhQki4CCkcpvK+B8lbMSPNVKXfQivoN9aJDQtPpEE9UFnheUpS8iSJdTwff2dEhftKdWSGeR89WXZZUDau38YXo6yCUfAgsJ597G9Kw5Sxihqr6q9QrbwOs5n9JbNhg8GtovR2e0l7I2e5xQsK2GUq+Sbb9RGxwSA6b2jmGGNoJ8HHxhvHW9+BMoS0QK0+o2s9g+aoum8HKnFJ/vWwg+vjfEB0NP/E40konreipbpuUe5LdG8Qa+cVf7ZQonbSvnHhtVL2geuuTqGrDwnSqYR06P3ZK/fV1qn7OjLdMhXAwg3ENuNfzuuNjIcXt8k8ps+oBCu+9CHl781TJO/WLi9LWBKknAbbJX73lSImncgyD6Q+pHL0inpDrQDCB0j1V2n59kK/PVsqEN6/VbXGnr+56+xyvnkqZUzuG3fS73jLjs9HX5yp+gTSmckIsl/vIcH2Jr6wpNoSiIN+PuAz6+mOEqRvB0gpVRgdmKhkaJM0w4tVmG2qrStzrCuUhTmlR+kMxXOx/E5cvnHXvri1YiTXZk+RpQo32bhQZF/itMfriTydRI81uO80omjnGPUU4Kg1F8uaYIFMKhmUoWjRDnuf3TeFEOk4bLNxc5Bf9C1KkaXXNJNx9/73BAvXonjb/ITw4Q1rFMBZ3ZukhTd5BuwDGB29HkpQHd34b98s3g4j145WDp55dIfNy1pzEn774FH86eVzm6ty7AjNHJSIhIRGjZq7AXplh4JC2Fob8+/AN2bZbkXTrABW7IGYGv6VMywTZEfjFRZyskaYCWrC3KA2j5Gn0MZhZZHbz2PcObH7rPMLnq3D5Aj6QV1UsxJo1WdBKaDRaZBYZka9eBBdNugvvcJfPpCTcGtzQAbprQElVAxq3L8Ikv6IQWE6uR1TOImYYzNr//iPeq5cyQM1/ErI318nruhxl2SGnIyNqM4SPceEDB4DpKFhTiGyttBxBmk5fBqO0ji3Wf869KN9hgS2iHd9qm1VlznkcJ//0KYSzv8EBmc0SbHx6GWYoS36yH8ezJZLub2Hnu+dC7KhWDJPytACLUqR2SDWdqDwO+jkCE6f9s7u92ZqDGcYKHLJYcfHrP4WjU4RYV4gUv3LjEyJ0XHFP+d86DmMC25lb0rHujA3lUptneBJPr5iFJNyCUWPH+QQoV7eOwQS50nyEKx3Blh0pAQfbZze8NTNQWOeA2LkbWZessFh2Y8PDq2GW26AOfHQtwl2yUZrt3LsTO375O9USqTCC/PogX5/t7oOu4+zRX6Neiu7NS6ntnITsp0wokdfa/grvtspbNMIkEr59DhpRMx7T5s2SlxpszcmCsWI/LPWX8PWKZnSKDtQVzgix4ekLdFz5SBZ564Qx3bbJ3vZleibunBZuk4oGt44Z55Z37go6Qs3SBzUm+M0Q1St44Fjf1WjT8UBhGd6VFoZ2tKKh5heqxf77o1ig+jdcPKU+LsGXEdqJY/EVrwEqkPK9L/DRxbPuBsUbxv/CefkqPlHfmjgWo7z0voopab1ddD0OY0cpC2NvwYQpyW5HTp1msOuPLuKUvPip68OghS9Yg9k1KqanTcEE7/1AXoGcvQE9F8raMeW+DndNHR+isihhBuJTyTfPmtZIVAjDW47eZf1M+Hz1dmTacRj7FW+BArwdk0epnqarTcbUicqayEgM66swgZtPpEX0dSgrzHa/BPklG1hOIitnETP0S8v95QvHeRwLcr/7WxG2Gd711GMxceyXVWJHYsyEUarvPb3suvlE7DiNmhIDnHtXY9G/Hu1+bdz0ZEyZoLQ56FLmvFy7dEw+3c+dugh3VxdK/1sxcexXfHV/whSkhXoZ9YoYgUmLnsab1e5BA+fe9ViyeDEWL8qALjEXJssZ1TpmbyQA3eeJcP5DHDkHTJ9/J6bJ1e0LdFx1r8vy7yPUcvv/Oujmk4g2THXHux1nzEXQJeqQsWgxFi9Wn8QwChPGhHNAesChy+YTZTPfX7G3eC3+NYJNPeH7IF/f7stLj37etvMvOHXxb90oHb59DhpZMwWLNlahusTgHiBY/xAWL16MRRk6JGaVwqJea+4noLv2TB34Os5/2CT7JNrFs/F1VTVVh+qra1VP1FdJBMoV0G4t9ZzHo1oUn5SC7LxHsami2O0Qed5aA2P37PstGDXO7d44P7iAy15PWsCn1664t3vLAjX4ythx7hHE6eWwfa7sAlN9RlQpe6bdYA597siHOB+S15cxdqJ7IWzQBsy7e06xMIYNjiIyJp+3IjVroTxi7dxnwTveXcfKLksp//+MmgJVT/aVsZgoj+TpUW7r8OwWVJUTsWc73zSjxnnK+1lcuKza9fzpNXykftntaboRvgDEBGPMhASWk8jKWcQMg+h5i24a3GPzV3C1RyNDEbYZmq9g3HSpwDjwwYWPVcdJXMe1jzqCaNSLW0kzsHDpfLk8uUdVupF1rgkfnleNEAWUOS/XwHDw6e7feXeTXk8ea7RIN0qDBpJD8S5qamrwRnkBtKjH1sXP4WDQ89+6e6FWRpnSsXj2FMh9rXABRw8cBSLdJdoTGwZhWMF+CGvl2Q1p1P4N1EqnMHzuGUXtU32lzXwGLL0/VR5pqzl5sZuRZiB8H+Tr2/3DAfCW49uQNuWrfWKVRpsJY5k0q3ANrQ21qKl5HeUFs4DGLVi85lCIY46UgYhIVPoILe+dHLByOQCOobK9WoLzBp7ZVOXZoSbt9GnB3pf2uEfutHdj9tdDTYCpGuUjVhyXO3TpbEQzXt6rHj4bieS534Xk16P+AKob2+SGWXAeR9WeN91TzHIeqXQ6twcv7XWfWSefHyTvpM2AyTowxxb4ipDSSZ7Dkbd+hzbJaRPaYH15F/b6AsXuqv4Aqmrdb+aCswEvvlAt83K/vYxDRq5BdqTPVf4Me89I+/Yk/p5dsLpSWP2mU2OnVmwlaZD0jTysKZwFOHdg8cPP+u96kw/ePYDD0hCD8qccZYFGVL5UgzPSoaJSPpS6dyjrTNbuR2oUWdLMR/I9WCbvxD+KfdX/5Z5iEZxoqtqDffL0jidwjNNVqTCILyMrZxEzDGbpP96OeYH84RlVkZYJ5JpDNPIRthmaqZi7bK580kL9vgNolKd4b8LZdAB75N2JwZSK8p7Qhvdrjrjbz3unQdftKMNR7Kv6T/cPCqjLnKft9XGV2ukD7rIu1/MdeGGrtJzifqzKmu52sKJUOWg04SIsRdIPH+iQVdqAjmQ98vLykPfDB3CfenlFkMheZ/bTK7j2qffN1hPShUut51U7QgW4fv829klH2xSW4gn9eJ9Er3MxAeO8Mzm+x0PzSoDr0lmckpTXfh1zchfigfS/x3+//x94S9XE9ZVtUr9b81arvKzi3mn/0H258euDfH22uw9S9+3bsKnac86s1Ba/WIatUtupX4is1FA+RPRWCm0WFMknfeSi1NqB5OwHkJf3IH74wDz34FJI0T5n9tOPrqkGpoJEaP8TTsj9zjSkTnYfTBMklOeWaqBr+jjVTGboGN0+CbYgUX0v1OJEdZieX6sXIQdZZOu3mFS9gxkiPIu/fRs+1PHTRb0+YOeueiNHsAWx3sXkvg0EgYt+fQuvVQtjvYt+JeuVRcOqxdfeRb4e/bzpBNAKtjBW3lMSuLsrBLN79KJe3oWnLKxVdPFf1B508XyXhbW+uIEM5O/eXWuSycrGHDV/6VpZ1C3ZqSyIVi3cDTA/Fl97W0b9NiMFKyPSPe8CetUmm8Cw6k0Ivc1Xr2yFXQ/TDVXeegg8erZKWVLViZBphyknEZWzEHWjC8Ng9Ve9CSuwLKs2rCm7VD0y3RslImkz1Iv7A+W7v/s2XQQCUrio6rK3zgaX5a63vo0FgRLl796yGUzGLLGw5oJn8184NpHuSg7If6/+SnvlW5Dv1l0q7+F2Jas3LQWxLtyCfeWZvLnmc7GjtUYskTYMeDcF+eR5NzYoG3F8jyK+6nndUeqMKr+DphasHCtlJTzv8P2mspkimPwginjLkdJGdb/5RM5jZSNiEJH+m0+ClE91H6TekOSt60ocVR3w6qmUOfXmE9W9YP1u0H5ctRGqS7rq+hNoYKSbRCINp8j31aGINrUo0aTDMUOcOjMAI4aSrzoCk/Iq0Wx7E1XyPL3Pf9UWlOONhhrsKJQWBktDKtNw3wtPuw/Elb7flghcF6CZ9D1sfHOvZ02i9HZQgqqGXXj2/oC1fpopyNteg3p5GkISMAsF5b/G/23YErCGbzRmFG5DY0OVT6YnbOOOfM/Ca5+e3V6F0LvbeCED+K+7AbTQl1ShYXcp7o/9SxFQ8DpsNh9fbUEl6hs3I085yy9pFgp31KBBvXlIW4DyelXehbRlcD3QaO/Fk6/Ww1brmQ7wqieVlRMytLoAACAASURBVNdR09CKjnc3I09eQC9tnMrHjsYGv7Lr5rMNhfJmH6+ACC6kurAZjfWV3jIuy/q/9e5F8l4JsU7XK3hwX0RUziJlGMxUDZLSH8d+W417KsgTRGqHamzV2KhsWEu+Dy9USlOZ0p8Wt6ET1xFZm6GZtAjbG3/tky/XExsayuXj/IMpFfU9t967UZwe4swzP8kr8YbtqGetlPxrA3L93Z43xbMmUGKzFm+2vuuZxvVEltvaRrzpPWTXT2gPv4xE8n1rUSlNw8l/0kpwwZOufx0DQm1aUiXpHVk/j9ZL6t8qEtBuewf7nFoYfnoPrjz5DYxK/TEu3/8qWt981rMpSJHjG1mL+pBsRdQg+wzWb1bb/h2vrflOP5zbKLWnNbDtfxzp8kambuB01wdhLNLX7Udrwy99dUvpF1v3Y11EdaAbHYL246M96ap9BcUHqYGv/gTKVs0ynDqLSyF/wk7ZNKuFYdk9SO7WS1NGwiM8NDtQrWDfVc5j0MtQHmXQwLxJAgNAgGW076CTbd+xHTDJwUZQBkyZWCfsG23xHz1Rjg2K5PgZJawyghadjqw70XCLcLQyGtGDIk4EZcs7ShlJWZVOS1OOzVLOI47c0FBltFtfNJgzyXskQAIkQAIkMPgIaDA6cxGK9Vo41UdHKccGddlhHcQC5dcpDD9CkXrdYZCgvEUCPSMwDplLH4I+zK/qKMdEaQt/gNzk7naJq0bCNxZAH81PQAYxgI5hECi8RQIkQAIkMEQJJGXgMencVe9PhLXjTHW5/PvJylKk0JbdRNs7FuxzpqPEtDDkeYmh4/MJCYQjIC3PyJfPAfV7cXE1oSJLh+SKOjT9yoJ67eN45fnvBZzzGkSu8Be88/qbcGpXwPRgiu9YqCBBe3IrQRp0DBdB+h3FboKEi85nJNDnBFhG+w4x2fYdW0ruDwIfw2r6LnLkXdSe9KQjyc6sQ3q3u7Z7px/rTu/4DavYkmO4YBHWNzohrTHf83QR5str2vuWQqgySsewb7lTej8QCFW4+yHpuE+CbOM+i2lgHxFg3ekjsBQbMwKhyiinkmOGmIJIgARIgARIgARIYGgToGM4tPOP2pMACZAACZAACZBAzAjQMYwZSgoiARIgARIgARIggaFNgI7h0M4/ak8CJEACJEACJEACMSNAxzBmKCmIBEiABEiABEiABIY2gYh2JQ9tE6k9CZAACZAACZAACZBAMAKBRxJGdJJTYKRggnmPBAaKQKgt9wOlTzylS7bxlJu0pT8JsO70J22mFQ2BUGWUU8nR0GQcEiABEiABEiABEohDAnQM4zBTaRIJkAAJkAAJkAAJREOAjmE01BiHBEiABEiABEiABOKQAB3DOMxUmkQCJEACJEACJEAC0RCgYxgNNcYhARIgARIgARIggTgkQMcwDjOVJpEACZAACZAACZBANAToGEZDjXFIgARIgARIgARIIA4J0DGMw0ylSSRAAiRAAiRAAiQQDQE6htFQYxwSIAESIAESIAESiEMCdAzjMFNpEgmQAAmQAAmQAAlEQ4COYTTUoorTDrv1MA5VGJFssqI9KhmMFLcEhDMw5yYj13wGQtwaScO6IyC0WVCkWwqz/bpfUMF5DNuMaZB+wiohqxQWeyQtSDvsR7bBqEvwxDNhT7OT5cuPLL8MXgI30WZZDV2uGfaQjWIkYQavhYNVMzqG/ZIz12E3P4mf7qnGE+v34tN+SZOJkAAJDCkCwkXUPvdjmJ0BWrs+RG19In7w6imInQ6cWNiG1foXYW0P2VsCuIm2w/vwFu7HDofoiXcZGzIeRWXz1YAE+JUEBh8Boe0/8NzqHQisDmpNIwmjDs/ryAjQMYyMUy9DjURKYRVef3ULNhq0vZTF6CRAAvFH4CqaK8txbPwd8G8hruOc7TPMyf8mtFJrrdEis8iIfNSjznYlNAahDX8asxBr56cgSQolxVu7ARsNJ1F58CRnLEKT45PBQMDVhMrS9zF+/qzQ2kQSJnRsPglDgI5hGDh8RAI+AgLaraXQJXwfFRYLKpRpvYRcmPY0wdlux5EKI3TSVF9CGozbjsGpGtARnM2weJ9LYXJhMlthd6kC+RJzXwlONO8xIUuWKU0hmmC22uEKDMfvQ5yAAFfzXryEh1GcOyXAlpGYrv8mJqlaauHyBXyQ+hCWZo4LCKv6qvkn6PW3QRUN0IzH1Lt0qkC8JIHBSOAqmnfuB574EXInfimEgpGECRGVt7sl4NdudBuaAUhg2BOoxfqXbZj29DGI4g04Gu5B04o50M3YhJZvv4hLYic6Tq8DylfhmdqL7vVc0pvt8pU4nPgYmjtFiKKITsc6JO57DCt32oI7esJFWB41YIH1ayhz3IAoyf357Xjv4cVYa/HIHfZ5EScAXDbsfAl4YlUGRoU1SVqnbMaGTU6Y9j+O9KRomu+/x31zprtHEcOmxYckMBAElJek5ViVHurFJ5IwA6F7/KQZTcsSP9bTEhLoMYF0lDxbjLyU0QBGQJvxLWRqtTBs3IC1mVpooEFSyhzMS/sr3j5xDi4IaG+qRWWrAcaiu93TgfLM3rewIn82Go+0wNFl0FBAe+MurDbPxMani5CpHSHFQNKMfLz82gK8vXoXGsOuL+uxUYwwYASUkY+C8I5euxUm3Rik5hRh6973UXf8fPAXinB2tP8BdR98Fz8yBIwkhovDZyTQnwRUL0nyEohgaUcSJlg83ouYAB3DiFExIAlEQ0CD0dmb4XBsRObl92GxWGCxHILZ9ABSi94IIfAKbHX1cGqTMXWi5BQqfxokTU5GmrOb9WVKcH4OcgLSyMcvUTPtSRSnjw2v6+hslDmkkeYTqC4Bti5e0sOR46to/sWvMGHzI+Ed0PBa8CkJ9CGBq2jebcW0zavClNFIwvShisNENB3DYZLRNDNWBKYhdXLId9ngibhaYDbeiVGpy/Hyib/Ko39jc7fCVrUEOHUWl0KtM3RuQc6YRPdRI551hompRagPngrvDjUCLht212jx+KIp/msBw9ih0WbCuGU7qgzKiHSYwN5Hbgf04Lj/iVXdOaDeOLwggf4k4HlJmvJDLJqkfhlW6xBJGHV4XkdLgI5htOQYjwQiInAd9oPPo+jIPNRcuoB3yx5FXl4e8rIn4Vrr+fASDFVo9axJlNYl+v7ZUJY9PnxcPh3kBNxLDMq3LMLkRM85gwmJGJOzBU68gaLULyMh1PltmqmYu2xuxPYJbb/G7pa5eLZwFtcWRkyNAfuXwBU0Hfw/2LJ4KhKVzXYJE5CztRmoL0Jqog655v/C8W7D8BzYWOQbHcNYUKQMEghJwIVLkgOYNhuz5LWCnoDCJ7j68Y0QscYhI9cA7amTaHHeVIWR3pi3ISuh6wHIqkC8HBIEPEsM/Bz+Tlxr2AAtlqCq9TOIdYVICdpCS2XqWkSbSASnFdsPjsQP8hWnUIDrzCGYGz8eEpSo5HAhMB7ZZTbVy6/0IvwRGkrSAfkF2YG6wnmY322YGRGPvg8XstHYGbTZiUYQ45AACQQj4HHy6g+gurHNvUtZcKJp+3NYbW4JFkGeah6tX4lX7nsPq0t3o0l2DgW47LV4Yd0OoHwdlqaMDBGXt+OKgLQ7vSgDWaZ9aJbLwU04rTtQdnk51qs3kSjhKpo8m1Kk8mLBhuUPo7g4BzrVqOSomQcBXQ+XQ8QVVBpDAiQQjgAdw3B0YvbMcwZe4kwU1Tvh3JqDMRz1iRndwS1Ig9H6NXiz+i4cz5nsniaZ/BTev82I2pqSgMOMVZZopiBvew1em/dnmHRfQkJCIkbpD2PCmgPYX5zJKUEVqri+1HwVt997J1q3FiBDKge6R/H61e+h+lUjZoQ5rkZoq8Va/WJsbQzyuxGG72JuMl8s4rrc0DgS6AWBBFFauBTmT/ptzm6ChInNRyTQ9wRYRvuOMdn2HVtKjm8CrDvxnb/xYF2oMsoRw3jIXdpAAiRAAiRAAiRAAjEgQMcwBhApggRIgARIgARIgATigQAdw3jIRdpAAiRAAiRAAiRAAjEgQMcwBhApggRIgARIgARIgATigQAdw3jIRdpAAiRAAiRAAiRAAjEgQMcwBhApggRIgARIgARIgATigQAdw3jIRdpAAiRAAiRAAiRAAjEgQMcwBhApggRIgARIgARIgATigQAdw3jIRdpAAiRAAiRAAiRAAjEgQMcwBhApggRIgARIgARIgATigUBEP4kXD4bSBhIgARIgARIgARIgAX8CgT97fIv/4+DfAiMFD8W7JDAwBEL93uPAaBNfqZJtfOUnrek/Aqw7/ceaKUVHIFQZ5VRydDwZiwRIgARIgARIgATijgAdw7jLUhpEAiRAAiRAAiRAAtERoGMYHTfGIgESIAESIAESIIG4I0DHMO6ylAaRAAmQAAmQAAmQQHQE6BhGx42xSIAESIAESIAESCDuCNAxjLsspUEkQAIkQAIkQAIkEB0BOobRcWMsEiABEiABEiABEog7AnQM4y5LaRAJkAAJkAAJkAAJREeAjmF03BiLBEiABEiABEiABOKOAB3DuMtSGkQCJEACJEACJEAC0RGgYxgdtx7Gaof9yDYYdQmQfoImIcuEPc1OCD2UwuBxTEA4A3NuMnLNZ1gu4jibg5kmOI9hmzHN0zaUwmJvDxbMfU9wovnwflTI4TNgsn4cOqz8REC7tRQ6qd1R/uWaYWfj0w03Ph4YAjfhbNrh6St1yDJZYHeFK6w30WZZDR3LdEyzi45hTHEGE3YTbYf34S3cjx0OEWKnAycWXsaGjEdR2Xw1WATeIwESGC4EXB+itj4RP3j1lKdtaMNq/YuwtnftDGUH8hEDFlgcmGqsQYdoQ1n2+PCkhL/gndffhNMbSgvDsnuQzJbfS4QXg4WAANfv30Y98vCqQ0Sn4w0svPxj6F9oRKhXJaHtP/Dc6h2q8j1YbBnaerB56Ov8E9rwpzELsXZ+CpKktDRaZK7dgI2Gk6g8eDJkge9rtSifBEhgoAlcxznbZ5iT/01opZZYahuKjMhHPepsV/yVczWhcvlafHDXTjS/ug4PZnvaE/9QAd+kjtaCXeO345ooQpT/OVBXOANs+ANQ8evAExAuwnZtNvIztXL51GjvRpFxAbDvHdiCvChBqhOl72P8/FkDr3ucacD2oa8zVPNP0Otv82+INeMx9S5dX6dM+TEloEzJfR8VFotnKk+ansuFaU8TnO12HKkweqbs0mDcdgxO1aCP4GyGxfvcE89sDT9NIk0b7jEhS5kCzDLBbLXDFVO7KGzgCIzEdP03MUnVCguXL+CD1IewNHOcSq2raN75PCqnlWLz2nvdTqTqaejLK2g6+Drqt5Zhk9kCa7gp6tBC+IQE+odAl77yJi5fuIjU4kXIHK2qJLI2Up3YDzzxI+RO/FL/6DeMUgmkPYxMH2hT/x73zZnuHkUcaFWYfg8I1GL9yzZMe/oYRPEGHA33oGnFHOhmbELLt1/EJbETHafXAeWr8EztRfd6QXm0ZyUOJz6G5k73yE2nYx0S9z2GlTttwR094SIsjxqwwPo1lDluQJTk/vx2vPfwYqy1eOT2QGsGHewE2mG3mrFhkxOm/Y8jPcnXNAt2C0rXf478ez/Bvz3iXouoM27DkW4cPcH+K5RtbQZQj61Fi5GTugQmy5ng5W2w46F+w4uAyw6r+XlsOrsC+4szA/pJAa7mvXgJy7EqXf0CNbwQ9aW1vtanL1OhbH8C7X9A3QffxY8MASOJ/qH4bVASSEfJs8XISxkNYAS0Gd9CplYLw8YNWCtPgWiQlDIH89L+irdPnIMLAtqbalHZaoCx6G7vaI9G+y2syJ+NxiMtcKhGFt0mC2hv3IXV5pnY+HQRMrUjpHlGJM3Ix8uvLcDbq3ehMdjUyqDkRaW6JdBuhUk3Bqk5Rdi6933UHT+vct6u4+zRX6Nefxduv/M7KN5zCmLHKWyEGYaVVWgOszBfk1KIOlFaq2VDbVUJ9JKDuHgddnJtc7dZwgADRcAzMzMqFTlFW7D3+Ls4fjZghaHLhp0vAU+syghwGAdK5/hLl45hv+fpVTT/4leYsPkRv1GBfleDCfYTAQ1GZ2+Gw7ERmZffh8VigcVyCGbTA0gteiOEDldgq6uHU5uMqRMlp1D50yBpcjLSnEHWoClB+Dn0CIzORpm82P4EqkuArYuXqEaFXbjUeh7azFx8P9299gpJs7Di6SdhaCxH6UF7t7vYNdp0PFBYhgZHPTboubZ56BWQ4aSxp72UZmNse1GCaizWl8LSdtMD4Sqad1sxbfMq9p99WCzoGPYh3K6ipSHwX+LguP+JVeljuz7mnSFAYBpSJ8vbiCLX1dUCs/FOjEpdjpdP/FUe/RubuxW2qiXAqbO4FGrUx7kFOWMSfceMJCQgMbUI9ZGnzJBDiIBGmwnjlu2oMiijzQCEj3HhA0cXKzTJ92CZATjV6lCNLnYJ5ndDo83BU8+uCL2Y3y80v5DAQBIYAW16Prbs2giD87c40SqNGrr7z5opP8SiSeoX5oHUMz7TviU+zRqcVgltv8bulrl4tnAWh8AHZxb1gVbXYT/4PIqOzEPNpUrkeRu0j2E1nQeQHDpNQxVa3y5ECl/fQjOKtyeaqZi7bC7Q6jHMs1HN+cEFXBYA/zX4tyItVdeDtsQz4pwGTFatYYw3hLQnfgi4X4CqPNVB2kz1f7Bl6//Cli4mFiE18RkYqqx4m7vuu9Dp6Q12OT0lFmV4wWnF9oMj8YN8xSkU4DpzCObG7g6ojTJBRhskBNxTgUibjVnyWkGPWsInuPrxjRA6jkNGrgHaUyfR4lSmUKSg0hvzNmQlLIXZfj1EXN4e2gSk8nJNtTEtRFlwOdB6ajaWzZ3qf+JBWOMFuC79P6SbFvJlIywnPhw0BKRyfu4bmJMqrekej+wym+fYJeX4pY/QUJIOSC/RnTyKKVb5RscwViRDyhHgsluwYfnDKC7OgS5R+QWCRIyaeRDQ9XBaMmQ6fDA4CXg69voDqG5sc68HE5xo2v4cVptbQqiswWj9Srxy33tYXbobTbJzKJWjWrywbgdQvg5LU0aGiMvbQ4aAtPO8KANZpn1olvP4JpzWHSi7vBzrvRvT1GXh33BGWnYglZ+q1/FBsaocKLIqmjxTyzfhbP5PHPb+wpL0ixK/wKbGdKzRd3Mo9pABSEXjiYDQZkGRznP8l7QhT2iD9cWduFy6CgbvTEs8WTx4baFj2Md5I7TVYq1+MbY2+n57wJuk4buYm8wO3ssjLi+kjn0N3qy+C8dzJiNROpNw8lN4/zYjamtKoA1ls2YK8rbX4LV5f4ZJ9yUkJCRilP4wJqw5EOT4hlBCeH9QE9B8FbffeydatxYgQ8pj3aN4/er3UP2qETPUU72esrAnzYrsUYlISFyBmnErUd3lGI8Aa6/9Dv+aoZPLnM74Eo65svHs8/O9O+MDQvMrCQwoAc2YFNw734Gt0vFfiQnQPfJvuLp4O17l0qt+z5cEUToOP8yf9Pua3QQJE5uPSKDvCbCM9h1jsu07tpQc3wRYd+I7f+PBulBllCOG8ZC7tIEESIAESIAESIAEYkCAjmEMIFIECZAACZAACZAACcQDATqG8ZCLtIEESIAESIAESIAEYkCAjmEMIFIECZAACZAACZAACcQDATqG8ZCLtIEESIAESIAESIAEYkCAjmEMIFIECZAACZAACZAACcQDATqG8ZCLtIEESIAESIAESIAEYkCAjmEMIFIECZAACZAACZAACcQDATqG8ZCLtIEESIAESIAESIAEYkCAjmEMIFIECZAACZAACZAACcQDgYh+Ei8eDKUNJEACJEACJEACJEAC/gQCf/b4Fv/Hwb8FRgoeindJYGAIhPq9x4HRJr5SJdv4yk9a038EWHf6jzVTio5AqDLKqeToeDIWCZAACZAACZAACcQdATqGcZelNIgESIAESIAESIAEoiNAxzA6boxFAiRAAiRAAiRAAnFHgI5h3GUpDSIBEiABEiABEiCB6AjQMYyOG2ORAAmQAAmQAAmQQNwRoGMYd1lKg0iABEiABEiABEggOgJ0DKPjxlgkQAIkQAIkQAIkEHcE6BjGXZbSIBIgARIgARIgARKIjgAdw+i4MRYJkAAJkAAJkAAJxB0BOoZxl6U0qHcEBLjsFpiydJBOhU/INcMu9E5ir2MLZ2DOTUau+QwGWpVe20IBJEACJEACg5oAHcN+yh7BeQzbjGluZyOrFBZ7ez+lzGR6RECw4+Ca1dg37RVc6hQh1hUihbWkRwgZuGcEum0b2q0w6RLcbYf0suL9p4vgZaEdduthHKowItlkBVudnuUNQ/c3gZtwNu2AUS7vOmSZLLC7Al+H22E/ss0TJgEJOiMqjtjh6m9V4zg9dnn9kbmuD1Fbn4gfvHoKYqcDJxa2YbX+RVjbAwt8fyjDNCIiMH4sRrF2RISKgXpBoNu2QUC77R3scwZLYy6WzZ2K0MX0OuzmJ/HTPdV4Yv1efBpMBO+RwKAhIMD1+7dRjzy86hDR6XgDCy//GPoXGlUvNDfRZimF3tiCedZrEEURnc0P48rmR/CC9eNBY8lQVyR0mzLULRs0+l/HOdtnmJP/TWgl2hotMouMyEc96mxXBo2WVAQQ7GbkJs5EUb0Tzq05GJOQAZOnsRGcTdhjyvWM1khvsmZYvaO+AtqtpdAlfB8VFgsqlJHhhFyY9jTB2W7HkQojdPJITxqM247BqXonEJzNsHifSyNCuTCZrUHelFW5JDjRvMeELGX0KMsEs5VvzSpCQ+AykrbhCmwnJ+A1xw25E5Q6QvnftQaU3P9dzE0eGcbOkUgprMLrr27BRoM2TDg+IoFBQEC4CNu12cjP1MovOxrt3SgyLgD2vQObMoginEfdLguQ/xAenDFaVlqj/RZW5E/Cvro/qBzIQWDPEFaBjmGfZ95ITNd/E5NUpIXLF/BB6kNYmjmuz1NnApET0KQUoq7zNKoMWmhLGnBNtKEsezyENgseTS+CdeJzcEjTy+IZ/Dz1GB7Wl8LSdlOVQC3Wv2zDtKePQRRvwNFwD5pWzIFuxia0fPtFXBI70XF6HVC+Cs/UXnSvF3Q1oXL5ShxOfAzNsmzpTXkdEvc9hpU7bcGnR4SLsDxqwALr11AmOwyd6Pj57Xjv4cVYa/HIVWnFy8FKIIK2QRAw+ftFyNaOUBlxHfZDVfgg7x4kq9oVVQBeksDQI6D5J+j1t6lGwG/i8oWLSC1ehMzRnoKuGY+pd+ngbPoQf/JOMbtwqfVT5OfeAberOPRMH2was1np1xyR1vuYsWGTE6b9jyM9ifj7FX9UiX2Mxpc2w5z2JJ5ee6971BejMaOwDK/l/xarXzqqektNR8mzxchLkZqnEdBmfAuZWi0MGzdgrfwWrEFSyhzMS/sr3j5xDi4IaG+qRWWrAcaiuz2ypUFl6Q14NhqPtMChGll0qy+gvXEXVptnYuPTRciUHQYNkmbk4+XXFuDt1bvQqLxdR2UvIw0MgRBtg+YfkDI9oLsTLuCoZQJW5k5TdaIDozVTJYE+IeCyw2p+HpvOrsD+4kwkeRMZh8ylD0HfWIwFj+/DGdd1OK3VqJu4Af9bP94bihe9I0DPpHf8Io8tLyAfg9ScImzd+z7qjp8PPhoUuUSG7A8C7X9A3b5maO+aiol+tSUJk1Onwame5uixPhqMzt4Mh2MjMi+/D4vFAovlEMymB5Ba9EYIaVdgq6uHU5uMqRPVo0gaJE1ORpqTSxRCgBu8t3vYNghnfwPLPy/Edyap83/wmkfNSCByAp5lOaNSkVO0BXuPv4vjZ9VbpjRISn8c+0+8gvlHVmDmqGlYceF72PKk8tIeeUoMGZqAX1cXOhif9JrA6GyUyQtqT6C6BNi6eAmn/XoNtf8EuNccqneEfjmI8zYNqZN977YRaedqgdl4J0alLsfLJ/4qLULF2NytsFUtAU6dxSXvdEmANOcW5IxJVO1QTUBiahHqA4Lx6xAg0KO24TrOHm3CP3PabAhkLFXsOQHPy7K0FMe2FyWoxuIuS3Zuwaixk5FWvAUleqC+aC2esbbxKK+eww4Zg45hSDR980CjzYRxy3ZUGZTpxL5Jh1JjSUALQ9VpdCoL/9Wfjs3IVta/9DjJ67AffB5FR+ah5tIFvFv2KPLy8pCXPQnXWs+Hl2aoQqtnTaJ3Q4Ksl3tdZPjIfDoYCUTUNsjTyP+A3AyuTx6MeUidYkVgBLTp+diyayMMzt/iRKsyaijAdWYf1lZ24ofFT6Gs4Xdo2ABsyVmJyuarsUp82MuhYzgQRUAzFXOXzR2IlJlmTwmMvgO5+TqcOvZHv53EwFU0V3yvlwdgS4umzwNpszFLvblA+ARXP74RQtNxyMg1QHvqJFqc6o0vAlzN25CVsBRm+/UQcXl70BPopm1wTyPrkRH1y8igJ0AFScBLQJN8D5YZvuT9Dumc2bUv4FLm7Z5TPiYhe/MB2MqB9aWWgf8xAp+mQ/qKjuGAZJ/kEFzDfXOmqxbVDogiTLRbAuOhf6IU9739Y5RuV46ZaYfdshXr1gPlm/N6cQC2x8mrP4DqRs9UiOBE0/bnsNrcEkIzDUbrV+KV+97D6tLdaJKdQ+nXWmrxwrodQPk6LE0Jd4RJCLG8PUgIhGsbOI08SDKJavQXAZcDree+gTmpng1Y0vdTgSdyjsbXZ98BHsgUu0yhYxg7lsElSUeLFGUgy7QPzXInfhNO6w6UXV6O9Qb11vzg0Xl34AloJi3C9sbtmHf5eegSpXWGY6A/PA5rbLtRnD62FwpKTt4avFl9F47nTEaidCbh5Kfw/m1G1NaUhG7oNFOQt70Gr837M0y6LyEhIRGj9IcxYc2BgB18vVCNUfueQE/bhnDTyIqsiiZuauv7nGMKfUBAOhasSOc5+1U6jUFog/XFnbhcugoGZaPV6NlYWjwb9c+Uo/qMZ3rZ9Ucc2nMc963M4fFNscoXsZs/QDpPlX/R3PAIhAAAIABJREFUE7gmnq4qFLWAKLGEtkAsr7GJjs7oJTKmPwGWUX8esfxGtrGkGSirZ21DZ2u1WFh+QuwIFCN977wg1hSmi3q/553itYYNvrZHboOWiFWtnwWTwHsxJsC600OgHafEqoJZ7n4SELUF5WKNzSF26So7HaKtukTUq/vU+tbg9aKHKgy34KHKaIIEIpyTKf0uZzdBwkXnMxLocwIso32HmGz7ji0lxzcB1p34zt94sC5UGeVUcjzkLm0gARIgARIgARIggRgQoGMYA4gUQQIkQAIkQAIkQALxQICOYTzkIm0gARIgARIgARIggRgQoGMYA4gUQQIkQAIkQAIkQALxQICOYTzkIm0gARIgARIgARIggRgQoGMYA4gUQQIkQAIkQAIkQALxQICOYTzkIm0gARIgARIgARIggRgQoGMYA4gUQQIkQAIkQAIkQALxQICOYTzkIm0gARIgARIgARIggRgQiOiXT2KQDkWQAAmQAAmQAAmQAAkMMgKBv253SyT6BUaKJA7DkEB/EQj1sz79lX48p0O28Zy7tK0vCbDu9CVdyo4FgVBllFPJsaBLGSRAAiRAAiRAAiQQBwToGMZBJtIEEiABEiABEiABEogFATqGsaBIGSRAAiRAAiRAAiQQBwToGMZBJtIEEiABEiABEiABEogFATqGsaBIGSRAAiRAAiRAAiQQBwToGMZBJtIEEiABEiABEiABEogFATqGsaBIGSRAAiRAAiRAAiQQBwToGMZBJtIEEiABEiABEiABEogFATqGsaBIGSRAAiRAAiRAAiQQBwToGMZBJtIEEiABEiABEiABEogFATqGsaDYQxlCmwVFuqUw26/3MCaDxy0B4QzMucnINZ+BELdG0rBgBATnMWwzpkH6eaqErFJY7O1dgwlONO8xIUsKozNiW5MzonIiOJuwx5Trlq0zouKIHa6u0nmHBAYHAZcdRyqM0EnlPEGHLNM+NDtvBujWDvuRbTDqpDDu+sByHYCol1/pGPYSYI+jCxdR+9yPYXb2OCYjkAAJxBsB14eorU/ED149BbHTgRML27Ba/yKs7erXg6torvwR1rV+B/s7RXQ2P4yPTD9CZfPV8DRcTahcsQtXFlejU+xEhzUbp4yLsdZyMSKnMrxwPiWBGBMQLuLwbiuw8GU4RBGdjjew8PJWZCzfgWaXUh9uos1SCr2xBfOs1yBK4ZofxpXNj+AF68cxVmj4iqNj2K95LzXw5Tg2/g5o+zVdJkYCJDD4CFzHOdtnmJP/TWilllijRWaREfmoR53tilddwW5BaeVMPPtUjhxOo83BU8/ORGWpBXalv/SGVi6uw36wApV3PYSiTC000CBpxg+x+ZV5eHv1LjT6OZ5KHH6SwMAREP6/SxiztBDzU0bLSmi092Lt00/C0Pg6DjZ56oNwHnW7LED+Q3hwhhLuW1iRPwn76v6AIGPtA2fQEE6ZjmG/ZZ4AV/NevISHUZw7pd9SZUKxIiCg3VoKXcL3UWGxoEKZ+kvIhWlPE5zt6imQNBi3HYNT1WkLzmZYvFMk0hRILkxmK+zeN+EgeqqnD+VpRhPMVk4FBiE1RG+NxHT9NzFJ1QoLly/gg9SHsDRznMem6zh79NeoT0vG5CQloAajM76D/FO/xtGzIZajCBdw9MBJpKXqkOSlMwLaWbOR5vR3PL2PeUECA0hAM/1e6CeN8NNAM3Eq7lKPomjGY+pdOjibPsSfvG2nC5daP0V+7h1wu4p+IvglCgJKSxNFVEbpEQGXDTtfAp5YlYFRPYrIwIOLQC3Wv2zDtKePQRRvwNFwD5pWzIFuxia0fPtFXJKm7E6vA8pX4Zlaz5SdNKW3fCUOJz6G5k7RPf3hWIfEfY9h5U5b8DVfwkVYHjVggfVrKHPcgCjJ/fnteO9hTgUOrvIQK23aYbeasWGTE6b9jyNdcQJlB+8otHdNxcQurfVRHDh6Ifi0sMuB1lOfdlHO3dE68MGFj4PH6xKDN0hggAnc+k3MSVVcvnHIXPoQ9I3FWPD4PpxxXYfTWo26iRvwv/XjB1jR+Em+S1MTP6YNJkuuonnnfuCJAl+DP5jUoy49IJCOkmeLkSdPd4yANuNbyNRqYdi4AWuVKbuUOZiX9le8feIcXBDQ3lSLylYDjEV3u6cM5VlDafpjNhqPtMChGll0KyKgvXEXVptnYuPTRcjUSm/R0lRgPl5+bQGnAnuQW0MiaLsVJt0YpOYUYeve91F3/LzvZUF28BAw8heBVUk6pKYB9Qd+g7NdypcOd00dDzb+EXBkkAEkIKDd1ogPVhXA4B1J1CAp/XHsP/EK5h9ZgZmjpmHFhe9hy5P3etvWAVQ4bpJm29DnWSlNIf8SNdOeRHH62D5PjQkMNgIajM7eDIdjIzIvvw+LxQKL5RDMpgeQWvRGCGWvwFZXD6c2GVMnqqdWNEianMypwBDUhuzt0dkoc0iL7U+gugTYunhJ7zeIaFLwoGkFtPXbsKm6xe1oSksT/r0OTc5pSJ3sm2AestyoeHwTcNnwiz3jsXlVhmo5hGTyLRg1djLSiregRA/UF63FM9Y2joDHsDTQMYwhzKCiXDbsrtHi8UVT+IYeFNBQuxlFp+pqgdl4J0alLsfLJ/4qj/6Nzd0KW9US4NRZXPKulQlg4dyCnDGJ7iMZ5OMbEpCYWoT6gGD8Gh8ENNpMGLdsR5VBGW0G4Bn5O9Xq8I0iRmSu9ELyFBrrC4Fn0jAqIQ3Gynfw4R8/QKPhu5ibPDIiKQxEAgND4Cqad7+NcRtWBMyyCXCd2Ye1lZ34YfFTKGv4HRo2AFtyVna/S39gDBmSqdIx7NNsc08jlm9ZhMmJnjOXEhIxJmcLnHgDRalfRkKuOczOwj5VjsL7hYC0O/R5FB2Zh5pLF/Bu2aPIy8tDXvYkXGs9H14DQxVaPWsSpWMZfP9sKMvmeprw8IboU81UzF0216d84HfPE3mTinMuls2dGuaFczRS5j+JPQ6p7JzCnuL/AXzgQolpIVLY8vsY82qQEbiJtsO/RMt9T6LQs/PYq6Bgx8G1L+BS5u2enfyTkL35AGzlwPqwu/S9EngRAQE2DxFAij6IZxrRr1PvxLWGDdBiCapaP4NYV8hGOnrAQyCmtGPuPJA2G7PktYIelYVPcPXjGyH0H4eMXAO0p06ixe9wV2lZwjZkJfBw9BDg4uC2VF6u4b450z3TZyORPPe7SNv3DmzeI2YEuC6dxamejPwJbbA+sw775m/Ds3ypiINyEq8m3ITTasbBUQuQ73UK23Fmzz73EUtBN1WNxtdn8wi4WJYIOoaxpElZJNCFgMfJqz+A6kbPOhjBiabtz2G1uaVLaPcNDUbrV+KV+97D6tLdaJKdQwEuey1eWLcDKF+HpSmcCgwBb+jclnaeF2Woft1B6hR3oOzycqw33OYdCdSk5GFz8Wm88GKDfASS4GzAiy+cRvHmPN9LpSKroilgylna7XwAFY88jD0TNmB/cWbAeq2hg4uaxjuBdtgtP8HynP+F4pzJSPQsn0lIGIOZ+z+HTtqpP3o2lhbPRv0z5ag+4zm10PVHHNpzHPetzEEyPZqYFBJijAlGCiGBUAQkJ28N3qy+C8eVxm7yU3j/NiNqa0pCH3SumYK87TV4bd6fYdJ9CQkJiRilP4wJaw6wcw+Feqjd13wVt997J1q3FiBDymPdo3j96vdQ/aoRM5TjamSbxiK9+Gcom/Aa0hMTkLj8HaRW/KybzWwfw2rKQELCDKys+wSznz6MPdy5OdRKyDDS1/OLJou3oLGL1VoYlt3jcfqkurAbti3jsW/mGPf665RyXHl4F7bncR1/F3RR3kgQpYVLYf6k3yLsJkiY2HxEAn1PgGW07xiTbd+xpeT4JsC6E9/5Gw/WhSqjHDGMh9ylDSRAAiRAAiRAAiQQAwJ0DGMAkSJIgARIgARIgARIIB4I0DGMh1ykDSRAAiRAAiRAAiQQAwJ0DGMAkSJIgARIgARIgARIIB4I0DGMh1ykDSRAAiRAAiRAAiQQAwJ0DGMAkSJIgARIgARIgARIIB4I0DGMh1ykDSRAAiRAAiRAAiQQAwJ0DGMAkSJIgARIgARIgARIIB4I0DGMh1ykDSRAAiRAAiRAAiQQAwJ0DGMAkSJIgARIgARIgARIIB4IRPSTePFgKG0gARIgARIgARIgARLwJxD4s8e3+D8O/i0wUvBQvEsCA0Mg1O89Dow28ZUq2cZXftKa/iPAutN/rJlSdARClVFOJUfHk7FIgARIgARIgARIIO4I0DGMuyylQSRAAiRAAiRAAiQQHQE6htFxYywSIAESIAESIAESiDsCdAzjLktpEAmQAAmQAAmQAAlER4COYXTcGIsESIAESIAESIAE4o4AHcO4y1IaRAIkQAIkQAIkQALREaBjGB03xiIBEiABEiABEiCBuCNAxzDuspQGkQAJkAAJkAAJkEB0BOgYRseNsUiABEiABEiABEgg7gjQMYy7LKVBJEACJEACJEACJBAdATqG0XGLIpaAdmspdAkJkH6GRv6Xa4ZdiEIUo8QfAeEMzLnJyDWfAYtE/GVvpBYJbRYU6ZbCbL8eEKUdduthHKowItlkRXvA09Bfo40XWiKfkEDfEbgJZ9MOGHVSH6lDlskCuyuwRbwJZ/M+mLJ0cj+qM27DEXvkNaLvdI8fyXQM+ysvhb/gndffhNObnhaGZfcgmTngJcILEhjWBISLqH3uxzD7GgkPjuuwm5/ET/dU44n1e/FpxJCijRdxAgxIAjEkIMD1+7dRjzy86hDR6XgDCy//GPoXGlUvQgJczTuw4qV2LN5/AaJ4DdZ5LTDqS2FpuxlDXYa3KLol/ZL/UoG3YNf47bgmihDlfw7UFc4AM6BfMoCJkMAgJ3AVzZXlODb+Dmi7aDoSKYVVeP3VLdho6Pq0S3DvjWjjeQXwggT6j4BwEbZrs5GfqZX7RY32bhQZFwD73oGt3TNqKNhxsPQQ7jIuQ6Z2BIDRmLHiObxy33tY/dJRlQPZf2rHY0r0S/olV6+g6eDrqN9ahk1mC6wc9u4X6rFNRFkK8H1UWCyoMKZ5lgTkwrSnCc52O45UGD1LBdJg3HYMTtUMiOBshsX7XJomyYXJbA0yTaLSWnCieY8JWcrSgywTzFY7XKogvIwHAtIoyF68hIdRnDslHgyiDSTQcwKaf4Jef5tqsOQmLl+4iNTiRcgc7XZVhLO/wYH6SUidnOSTr/lHzLp3JpxqB9L3lFdREKBjGAW0nkYR7L9C2dZmAPXYWrQYOalLYLKcYQffU5CDInwt1r9sw7Snj0EUb8DRcA+aVsyBbsYmtHz7RVwSO9Fxeh1QvgrP1F50rxd0NaFy+UocTnwMzZ3uEeNOxzok7nsMK3fagpcD4SIsjxqwwPo1lDluQJTk/vx2vPfwYqy1eOQOCh5UotcEXDbsfAl4YlUGRvVaGAWQQBwQcNlhNT+PTWdXYH9xJtxuoADXpbM41cW8EZg4NRla51lcuMzp5C54orhBxzAKaD2NokkpRJ0orZmwobaqBHrJQVy8Djubr/ZUFMMPOIF0lDxbjLyU0QBGQJvxLWRqtTBs3IC18hSIBkkpczAv7a94+8Q5uCCgvakWla0GGIvuhtZT4zTab2FF/mw0HmmBQzWy6DZPQHvjLqw2z8TGp4s8UyYaJM3Ix8uvLcDbq3ehUZlaGXAeVKB3BK6ieed+4IkCpCexOe4dS8Ye+gQ8MzOjUpFTtAV7j7+L42eVjSUaJE1ORhqO4sDRC1036WmTMXWiNL3Mv94SYEvUW4I9iK/RpuOBwjI0OOqxQX8SlQdPck1ED/gNzaAajM7eDIdjIzIvvw+LxQKL5RDMpgeQWvRGCJOuwFZXD2eXhs7TMDrrUWe7EiIubw8dAtIU8i9RM+1JFKePHTpqU1MS6DMCnvZSmo2x7UUJqrFYtbFEk7IQphId6p8pR/UZt8MoOG3497pmONOSMZkvVzHJGTqGMcHYMyEabQ6eenaF/6Lanolg6AEjMM1/fUskerhaYDbeiVGpy/Hyib8C0GBs7lbYqpYAp87iUpfjGDxCnVuQMybRd7xRQgISU4tQH0maDDP4Cbhs2F2jxeOLpqjWVQ1+takhCfQ9gRHQpudjy66NMDh/ixOtyqjheGQ/ux/1xV/gmZljkKAzovLYh/hj0zme8hHDTKFjGEOYkYvyjPzwDSdyZEM25HXYDz6PoiPzUHPpAt4texR5eXnIy56Ea63nw1tlqEKrZ02ieye7sqPdhrLs8eHj8ukgJ+BeYlC+ZREmJypnmyZiTM4WOPEGilK/jASeczrI85Dq9TUBTfI9WGb4kn8ySSmYv24PHNLpHo49KL4jER+0LoXpwRS+YPmTivobHcOo0fUmorSI9v8h3bQQKcyB3oAcAnFduCQ5gGmzMUs+XsGjsvAJrn58I4T+45CRa4D21Em0ONWLqaWpx23ISgh2AHIIUbw9SAkoU2aKsy99duJawwZosQRVrZ9BrCtk+zBIc49q9RMBlwOt576BOanSmu6uf4LzCJ5Z+Sbmv1mCbM/O5a6heKenBOiW9JRYj8NLp7T/Jw43Oz2LZaWT3X+BTY3pWKPnqE+PcQ65CB4nr/4Aqhvb3GVAcKJp+3NYbW4JYY0Go/Ur3Wdzle5Gk+wcCnDZa/HCuh1A+TosTRkZIi5vD0sC0i72ogxkVTQF3+U+LKHQ6KFEwP2rP57jv6QNeUIbrC/uxOXSVTBMCthUIu1aPlSBR771GiaU/YxrdGOc0XQMYww0qLhrv8O/ZuiQmJAAnfElHHNl49nn53t3qAaNw5txQkBy8tbgzeq7cDxnslwGEiY/hfdvM6K2piTIYcYeszVTkLe9Bq/N+zNMui8hISERo/SHMWHNAdXxDXGCiGZ0Q8CzUzNxJorqnXBuzcGYiEaNo43XjTp8TAJ9QEAzJgX3zndgq3T8V2ICdI/8G64u3o5XC2d5jqsB0G6FSfq5vFFrUNc+G09/8Cqe9ByI3QcqDVuRCaK0eCnMn/Sbvt0ECRObj0ig7wmwjPYdY7LtO7aUHN8EWHfiO3/jwbpQZZQjhvGQu7SBBEiABEiABEiABGJAgI5hDCBSBAmQAAmQAAmQAAnEAwE6hvGQi7SBBEiABEiABEiABGJAgI7h/9/e/UBFdd37Av8y5Blvi+j1auuMprFKwaSSWGFh/pg6YjI0r9EaiJqa4BjnJbpeTLzhKURi0nsTlfBn4TKpr+amjCiJqUbm4fXeJoxhSlyxFt5gTWBVmaJLe2GG92p8gpNEveWct878gTMDgwMcYObwZS2XM3PO2Wfvz95zzm/vs88ZBRCZBAUoQAEKUIACFFCDAANDNdQiy0ABClCAAhSgAAUUEGBgqAAik6AABShAAQpQgAJqEGBgqIZaZBkoQAEKUIACFKCAAgIMDBVAZBIUoAAFKEABClBADQIMDNVQiywDBShAAQpQgAIUUEAgrF8+UWA/TIICFKAABShAAQpQIMIEgn/d7rZw8he8UTjbcB0KjJRAqJ/1Gan9q3k/tFVz7bJswynA785w6jJtJQRCtVFeSlZCl2lQgAIUoAAFKEABFQgwMFRBJbIIFKAABShAAQpQQAkBBoZKKDINClCAAhSgAAUooAIBBoYqqEQWgQIUoAAFKEABCighwMBQCUWmQQEKUIACFKAABVQgwMBQBZXIIlCAAhSgAAUoQAElBBgYKqHINChAAQpQgAIUoIAKBBgYqqASWQQKUIACFKAABSighAADQyUUmQYFKEABClCAAhRQgQADQxVUIotAAQpQgAIUoAAFlBBgYKiEItNQkYAAt8OCvMU6SD8XFJNhhkMY5eIJ52DOSECG+RxGOyujLMHdU4ACFKDAMAswMBxm4F7JCy40HD2IEmMyYmJSkWe73GsVfjCKAoIDh1/YiIpZv0Rrlwixeh0S+S0ZxQpR/64F10ns8hwPYhCzOB8WR2cfhRbQacuHTuqs+P+F1WnphMN2FEdKjEjIs6GvlPvYGT+iwCgJ3ISrfg+MOqmd67A4zwKHO7g7fBOuhoruzrvOuAvH+/zOjFIRVLBbnvJGsBI9J4BnDFhqcWKmsRLXRDsK06eMYA64q7AFpkzCBH47wubiioMUcH+OKmssntzXCLHLibplbdiofxO2zqCTofAf+OT9Y3B170YLw6oHkNBvG70Oh/kl/PP+cry45QC+7t6WLygQiQIC3H/8CFZkYp9TRJfzQyxr/wX0b9TKOjQC3A17sPatTmQdvAhR7IBtUROM+nxY2m5GYqGiMk/9HlaiskSRmml3PUpXb8KZeXvRsG8znkhPRFyk5nWM5ktwmJERexdMVhdcRUswUTaiK7jqsT8vwzdaI/VkzbB191L9ozmPo8Ri8Y0GSz3eDOTtr4er04HjJUbfaE8yjLtOwiU77wuuBli6l/u2M9v66CnLKkYaed6fh8X+0aPFeTDbHHDLVuHLSBe4jvP2b7Ag+z5opSOxRos0kxHZsKLafkWWeemEacE7U3ajQxQhev45Ub1uDvo/gI9H4royvL+vANsNWll6fEmBCBQQLsHeMR/ZaVpPu9Zo74fJuBSo+AR2f0dJuqKTfwTzjKuQph0HIB5z1r6GXz76KTa+9ZksgIzA8kVRlvo/rkRRQSI7q1fRsPd1lM7Kx85ND3pPApGd4TGZO03iOlR3nUWZQQttbg06fCO6QpsFz6aYYJv2GpzS5WXxHH6VdBJP9+qlVmHL23bMeuUkRPEGnDUPoH7tAujm7EDTj99Eq9iFa2c3A8UbsK3qkne+oKfDsB5HY59Dgydtqae8GbEVz2H9XnvfgZ5wCZZnDVhq+x4KnTcgSun+6m58+nQWNll86Y7JGoy2Qo/HbP19mC47CgvtF3Em6SmsTJssK8wV1B9+H9aiQuwwW2QdEtkqfEmBaBfQfB96/R2yzs5NtF+8hKSc5UiL935JhJbf45B1OpJmyIZVNN/F3AfvgkseQEa7xSjnX3ZIGuWcqHj3gsOC/C3/iewHv8IHz0hzC2PAeRHRUuGXUfvWTpiTX8Ir3UF9POasK8R72X8I6qWmIPfVHGQmxgMYB23qQ0jTamHYvhWbPL1gDeISF2BR8pf4qO483BDQWV+F0mYDjKb7uzsMGu1DWJs9H7XHm+CUjSx6xQR01r6Djea7sP0Vk6/XrEHcnGy8/d5SfLTxHdT6e9fRQsx8ApDmApqxdYcLeQefR0pcz6FZcPwrCosaAFhRZMrCkqQVyLOc67vTQEsKqEHA7YDN/Dp2tKzFwZw039U1Ae7WFjT2Kt84TJuZAK2rBRfbeTm5F88gPug5+gxiY24SjsB1tHz2Maz6ebj73oeRs78R4rVGbIcZhvVlaOg1sTacNLnOiAl0foHqigZo583EtIBvSxxmJM0aYi9Vg/j0nXA6tyOt/QQsFgssliMw5/0MSaYPQxTxCuzVVri0CZg5TbqU4v/TIG5GApJdwZch/cv5f8QKdNqQp5uIpCUmFB04gepTFwKCPs9ItiiNJNtRVZYLvRQgZm3G3oarEVskZowCgxPwTcuZkIQlpgIcOPU7nGrx3zLlO8bhMxz67GLvJzT0OiYOLgfcCrJRW2oMk4Abrc0XoE3LwOMp3rkTiJuLta+8BENtMfIPO3o38GHKCZMdvIB3zqHsjtCYv+sjeJsVeIkjnN25m2A23osJSavxdt2X0kQzTMoogr1sBdDYgtZQHQdXAZZMjO25QzUmBrFJJljD2SfXiSyB+HQUeibb16E8FyjKWtHnlACNNgU/W1eIGqcVW/WnUXr4NOdURVZNMjdDFvB1lqWpOPYDyEU5smRTdjSJy5CXq4N1WzHKz3kDRsFlx/+qboArOQEzZCPtQ87KGE4gYAxkDDsMX9GFy7h4xtkrfU3CA1hlABqbnQGjA71W5AcRIKCFoewsuron/vtvABAhOnci3Tf/ZeAZvQ7H4ddhOr4Ila0X8bvCZ5GZmYnM9OnoaL7Qf3KGMjT75iR6b0bw54l3uvcPF7lLNdo0GAt2o8zgn2rQd1412iV4+dW1gZPy+16Vn1IgSgXGQZuSjYJ3tsPg+gPqmv2jhlOQ/upBWHP+hm13TUSMzojSk5/jT/Xnw7hLP0opRiHbDAyHG10zBTPn6eA6cxHtveaLfQvJSTrenTzcdTCU9OPvQUa2Do0n/xRwJzFwFQ0ljw3xAdje0WQkz8dczx12vowKX+Hq5Rshcj0ZqRkGaBtPo8kln08jPcZhFxbHrITZcT3Etvw44gU0M7Fw1cJbZNN3SY0jJLdw4uJoF/AOoNweWIy4RDyyeT+cUkfduR8598TiTPNK5D2RyEuggVKDfsfAcNB04W4Y4kTudqK5cT5WLZzJxhwu5aisNwX6F/Px6Ee/QP5u/2NmOuGwFGHzFqB4Z+YQHoDtaxvWQyivbfNOKRBcqN/9Gjaam0KUVoN4/Xrv4xny30W9JziUfq2lCm9s3gMUb8bKxPEhtuXHkS8gdRY68OiC2f10GKVJ+P8XKXnLhtD2Il+COaQApPPk+R9hQZJ0Q1/vP8F1HNvWH8Mjx3KHcOWmd7pj/RMGhsPeAuQn8g9wTpozJp38y97HmRyexIedX4EdaKYvx+7a3VjU/jp0sdI8w4nQH52MF+zvIidl0hD2ILWNF3CsfB5OLZmBWOmZhDNexok7jKiqzEXIJ89p7kTm7kq8t+gvyNPdjpiYWEzQH8XUFw7J7uAbQra46cgISI8dMqVicV4FGjwB/k24bHtQ2L4aWwz+x3ZIv/LwWxxtcPnmIku/DPEv2FGbghf0sofj+9MqqefUlJGpPe5FYQHpsWAmne/Zr9LVNaENtjf3oj1/AwzT5TfaAZDuWj5Sgmceeg9TC//nEI/DChdEDcmJt/gDpOep8m/IAteaRWvxGlELiIBBzC2vE51dQ06VCUgT7NhGh60d0HbYaEVR7BDPlq3zHRMgQrtGLK60Bx0XbojOmn8G3yEsAAAgAElEQVQS9Z7jBkTtmmLxw5pm8VpwtrouipXrUkR9cZ1sWZfYUbO1J31PGivEsuZvgrfm+2EQ4HdngKjXGsWyNXM9x3PJTmrrlXanGHCa7KgRc7W+c2hZjdh8LWDpAHfI1UO10RiJpr8AV3rm3i1W6W9zLqPAsAuwjQ4fMW2Hz5Ypq1uA3x11168aSheqjfJSshpql2WgAAUoQAEKUIACCggwMFQAkUlQgAIUoAAFKEABNQgwMFRDLbIMFKAABShAAQpQQAEBBoYKIDIJClCAAhSgAAUooAYBBoZqqEWWgQIUoAAFKEABCiggwMBQAUQmQQEKUIACFKAABdQgwMBQDbXIMlCAAhSgAAUoQAEFBBgYKoDIJChAAQpQgAIUoIAaBBgYqqEWWQYKUIACFKAABSiggEBYv3yiwH6YBAUoQAEKUIACFKBAhAkE/7rdbeHkL3ijcLbhOhQYKYFQP+szUvtX835oq+baZdmGU4DfneHUZdpKCIRqo7yUrIQu06AABShAAQpQgAIqEGBgqIJKZBEoQAEKUIACFKCAEgIMDJVQZBoUoAAFKEABClBABQIMDFVQiSwCBShAAQpQgAIUUEKAgaESikyDAhSgAAUoQAEKqECAgaEKKpFFoAAFKEABClCAAkoIMDBUQpFpUIACFKAABShAARUIMDBUQSWyCBSgAAUoQAEKUEAJAQaGSigyDQpQgAIUoAAFKKACAQaGKqhEFoECFKAABShAAQooIcDAUAnFW6XRaUOeLgbSz88E/tMhw3wOwq2253L1CwjnYM5IYHtQf033KqHgOoldxmTvsWFxPiyOzl7rdH8guNBw9CBKPOunIs92uXvRrV4IbRaYdCthdly/1apcToEIELiJNstG6DLMcASdJAVXPfbnZXi+MzrjHtS7bkZAftWTBQaGw16XAjrtn6DC1deOFmLVwplgJfRlw88oMAYE3J+jyhqLJ/c1Quxyom5ZGzbq34StM+hMCMATQD5jwFKLEzONlbgm2lGYPiU8JOESql77Bcx9HofCS4JrUWAkBYS2f8NrG/egV5N116N09etozjCjS7yBBuNl5K3egwZ37+/MSOZXTftiTDLstXkF9tNT8Z7zBkRR7PnXUYPcn/4ECxPGD3sOuAMKUCASBa7jvP0bLMi+D1rpSKzRIs1kRDasqLZfCcyw52S4CWfm7UXDvs14Ij0RcYFr9PPuKhpKi3Fyyj3Q9rMWF1EgYgSk9p5/AlMemRuUpetwHC5BaVoOXk6fDg3GQZv+PF5NO4L8ww5efQvSGuxbBoaDlQt3O0HAjMdNSNeOk21xHY4jZTiT+QASWAMyl0h+KaDTlg9dzOMosVh8l/KkqQEZyNtfD1enA8dLjNB5pgskw7jrJFyyDqzgaoCle7lvO7MNjv56udJlw/15WOyfgrA4D2abA+5IZmLeBiAwHrP192G67BggtF/EmaSnsDJtsiydq2jY+zpKZ+Vj56YHvUGkbGn/LwW4Gw7gLTyNnIw7+1+VSykQEQJSez8IvPjfkTHt9sAcCRfx2aHTSE7SyTpGk5GasQiNh36PFtkxN3BDvhuIgOyQNJDNuG7YAprvIHF2fODqUuO2TMX6jFm8jBwoEwXvqrDlbTtmvXISongDzpoHUL92AXRzdqDpx2+iVezCtbObgeIN2FZ1yduD9Yz2rMfR2OfQ0OUdNe5ybkZsxXNYv9fed6AnXILlWQOW2r6HQs9ocxeu/epufPp0FjZZfOlGgRazGK5AJxw2M7bucCHv4PNIies5NAsOC/K3/CeyH/wKHzzjnYuoM+7C8f7mIvp367Zj71vAixtSMcH/Gf+nQMQK+Dsyq7EhRd458mZYaPk9DlknYd7MKb3PndaP8VkL588qUbU9Rx8lUmMaYQlIjdvyw2V4eLp8FDGsTbnSqAukIPfVHGQmSsH+OGhTH0KaVgvD9q3YlKaFBhrEJS7AouQv8VHdebghoLO+CqXNBhhN93eP9mi0D2Ft9nzUHm+Cs1cvV0Bn7TvYaL4L218xIc0z2qxB3JxsvP3eUny08R3U9jEHbdRpmIHBCXhuTpuIpCUmFB04gepTF2Sdheto+exjWPXzcPe9DyNnfyPEa43YDjMM68tuMa/KP/KyJiDQHFwmuRUFRkBA1pHpPVVCgLu1BY2YhaQZvZeOQO7GzC4YGI54VUsH+nr8MOMeBI0jjnhOuMORENAgPn0nnM7tSGs/AYvFAovlCMx5P0OS6cMQGbgCe7UVLm0CZk6Tdx40iJuRgGRXH3PQQqTEj6NAID4dhU4RXc46lOcCRVkrZKPCbrQ2X4A2LQOPp0gdDwBxc7H2lZdgqC3uZ16VNPLyG1TOegk5KZOiAIFZpMBVNLxrw6ydG9iRGeXGwMBwpCvAcxn5O8hI7T1MPtJZ4f4GIzCI3qq7CWbjvZiQtBpv130p3WWASRlFsJetABpb0BpqnqGrAEsmxgY84ig2yQTrYLLNbSJeQKNNg7FgN8oM/tFm6Vbky7h4xtkr75qEB7DKADQ2O2Wji7LV3Ha8W6nF88vv7H3JTbYaX1IgMgR8HZk7f47lIa+k+TrGuIDmVs60Hs56Y2A4nLp9pO29jKxHajzp++BR4UfSXXSvw3R8ESpbL+J3hc8iMzMTmenT0dF8of/yGsrQ7JuTGHBH+0AeU9L/Hrg00gQ0M7Fw1cKeXGmmYOY8HVxnLqK915SDbwVNwvdv5p2+UFywHDNi/c9OjcXEJQVw4UOYkv4OMX08G86/Nf+nwMgLXEH94V+jIGsmYv0328VMxZKiBsBqQlKs95m/8HSIgm5IwU20X2yBy8CnfChVb4xOlJIMKx1eRg6LSVUreS8FInk+5srvTBe+wtXLN0KUVLrLzgBt42k0BTy4VepV78LiGD6kOAScCj6W2ksHHl0w23fXZYi24HaiuXF+iOeg+qYvyB+PJXaho2YrtFiBsuZvIFavQyKP/ipoL2opwhSkF9p7Hufmabt/RU1uCuDpIDtRvW4ONJ6O03RUVH+BnsfAS9+ZNhhW8SkfSrUGHhqUkgwnHV5GDkdJZev4TuzWQyivbfPepSy4UL/7NWw0N4Uoqwbx+vX45aOfYmP+u76n+gtwO6rwxuY9QPFmrEzk8y9D4EXPx9Kd56ZULM6rQIOnA3ATLtseFLavxhbDHb5LwPK28AHOSdMOpPZT9j7O5MjagT+tkvq+Ly1HjwpzSoF+BMYjceVm5NSX4k2bdDz1fmfeqH8CO1cmctpEP3IDWcTAcCBaQ1xXaKnDSf1jSONl5CFKRtPm0on9BRwrn4dTS2Z4L5PMeBkn7jCiqjI39AOHNXcic3cl3lv0F+TpbkdMTCwm6I9i6guHcDAnTfYMr2iyYF4DBDR/j7sfvBfNRWuQKtWx7lm8f/UxlO8zYo7scTXwtYX9yTakT4hFTOxaVE5ej3K2gwBOvhkjAnFpyDm4FVP3/wSxMTOxunoWSoIe8TRGJIatmDGiNHmpnz/pt31vsUo/W3MRBYZfgG10+IxpO3y2TFndAvzuqLt+1VC6UG2UI4ZqqF2WgQIUoAAFKEABCiggwMBQAUQmQQEKUIACFKAABdQgwMBQDbXIMlCAAhSgAAUoQAEFBBgYKoDIJChAAQpQgAIUoIAaBBgYqqEWWQYKUIACFKAABSiggAADQwUQmQQFKEABClCAAhRQgwADQzXUIstAAQpQgAIUoAAFFBBgYKgAIpOgAAUoQAEKUIACahBgYKiGWmQZKEABClCAAhSggAICDAwVQGQSFKAABShAAQpQQA0CYf0knhoKyjJQgAIUoAAFKEABCgQKBP/s8W2Bi/t+F7xR32vxUwqMjkCo33scndyoa6+0VVd9sjQjJ8DvzshZc0+DEwjVRnkpeXCe3IoCFKAABShAAQqoToCBoeqqlAWiAAUoQAEKUIACgxNgYDg4N25FAQpQgAIUoAAFVCfAwFB1VcoCUYACFKAABShAgcEJMDAcnBu3ogAFKEABClCAAqoTYGCouiplgShAAQpQgAIUoMDgBBgYDs6NW1GAAhSgAAUoQAHVCTAwVF2VskAUoAAFKEABClBgcAIMDAfnxq0oQAEKUIACFKCA6gQYGKquSlkgClCAAhSgAAUoMDgBBoaDcxvgVgLcjmqUGJMh/QRNTEwyjCXVcLiFAabD1VUrIJyDOSMBGeZzYKtQbS33WTDBdRK7/MeGxfmwODqD1hvs8aMTjuO7YNRJx5wYxCzOw/4GF9tXkC7fRpLATbjq9/jarA6L8yx9nCeD2rXOiJLjDrgjqRhRnhcGhiNQgUJbFTbpN6Nx0Qe4JooQuz6G8Uop9G/UIvgUMALZ4S4oQIFIEXB/jiprLJ7c1wixy4m6ZW3YqH8Tts6e7sHgjh830Xa0Av+On2KPUzrmSGm3Y2vqsyhtuBoppWc+KCATEOD+40ewIhP7nCK6nB9iWfsvgs6TN9FmyYfe2IRFtg6IooiuhqdxZeczeMN2WZYWXw5FgIHhUPTC2vY6Wqp/AzOWwvjE3YiTttFMh37tKiRXfAK77AQQVnJciQIUUInAdZy3f4MF2fdBKx2JNVqkmYzIhhXV9iu+Mg7y+CG04c8Tl2HTI4m+Y44WaZu2YrvhNEoPn2aHVCUtSFXFEC7B3jEf2WlaeL8O98NkXArIz5PCBVS/YwGyn8ITc+I9xddoH8La7OmoqP6C7VqhBsHAUCHI0MmMw7SZCdC6vsDpP/vHBwW4W1twPvthpMazCkLbRdISAZ22fOhiHkeJxSKbFpCBvP31cHU6cLzECJ1/qsCuk3D1DPpAcDXA0r1curSXgTyzrY/LJLIyCy407M/DYk+a3kuBZhsvmciEovzleMzW34fpskOA0H4RZ5Kewsq0yb6yDfL4ofk+9Po7PCfYbiTNFMycp+t+yxcUiCiBXm32JtovXkJSznKk+c+Tvjbsqv8cf+6eiuVGa/PXyM64B95QMaJKFZWZkR2SojL/UZBpDeLTliNHfxpblv4PmM91QnDVoKT6ezj4jwvZkKOgBgOzWIUtb9sx65WTEMUbcNY8gPq1C6CbswNNP34TrWIXrp3dDBRvwLaqS975XO56lK5ej6Oxz6GhS/Re/nBuRmzFc1i/19733BjhEizPGrDU9j0UOm9AlNL91d349OksbLL40g3MGN9FtUAnHDYztu5wIe/g80iJ8x+alT5+/AMeXTDbO4oY1V7MvKoF3A7YzK9jR8taHMxJk7XXyUhb+RT0tTlY+nwFzrmvw2UrR/W0rfhH/RRVk4xo4cRb/AHSeYx/QxXocn4mlq6ZK0qeMJSJzV1DTZHb+wVGpo12iR01W0UtUsTcmr/6dy2KHTVirlYrGsrOit1V2nVWLDNoRW1ujdgh+rbTbhVrOrrXEEXxG7G5bEVPW/BsM9uXjn9fK8Sy5m969hUyLdkqCr8cGVuFMx1tyXnaELzHBhjE3Mqz4rWgMihy/JD2YygV7dfk7TBoR3yrmAC/O4Oh9B/7fN8H/VaxsrkjKKEborPul+IarbRO0LE3aE2+7V8gVBv1d0tHNBgdizvTTPgH3JlsRHGuAbBuw/ptxwMuNY5Fk7FRZg3i03fC6dyOtPYTsFgssFiOwJz3MySZPgxBcAX2aitc2gTMnDZOto4GcTMSkOySz0GTLebL6BSIT0ehZ7J9HcpzgaKsFb1GhYd+/LiKhn/5V0zd+YxsNDI6uZhrNQv4jpfS1Rj7AeSiHFn6fFjabsoKfRsmTJqB5JwC5OoBq2kTttnaeLe9TGioLxkYDlUwnO3dTTBv2gf8/EVsLjwGZ816oMCI1aX1fV9GDCdNrjNKArOQNMNzC1H4+5fq33gvJiStxtt1X0p3GWBSRhHsZSuAxha0ds+VCUrSVYAlE2N9jzjyPnIkNskEa9BqfKsOAY02DcaC3SgzfImP6s73HBuGfPwQ4G74DQ5P/m/YkDJJHVgshcoFxkGbko2Cd7bD4PoD6ppl8/PPVWBTaRd+nvMyCmv+N2q2AgVL1vNuewVbBANDBTH7Tuo6HIdfh6k1CXO10ujPOGjTX8Ux+xZgSwkOO673vRk/VYmAr/6PL0Jl60X8rvBZZGZmIjN9OjqaL/RfRkMZmn1zEqXHMvT8s6MwnfNp+seL0qWamVi4aqEs80M/fghtH+PdpoV4dd1c2Vwt2S74kgIRKqBJeACrDLf35E5w4PCmN9CadrfvTv7pSN95CPZiYEu+BQ7ZDX89G/HVQAUYGA5UbMDrS3dMBQcAGsT94F6kaQecGDeIOgFf/SfP93UMfAUQvsLVyzdClGYyUjMM0DaeRpNLfglFGvnZhcUxK2FmhyKEXbR/LLWXDtkNIkM7fgguG3YfHo8ns/1BoQD3uSMw1/KZb9HeUsZE/t1ONJ//ERYk+e43lt43fh1U9Hj8YP494Ok0iGUIbxkYDgEvvE19d1FZd2FHeZPv8lAnzh15H5WPPomMhPHhJcO1olTAF+RZD6G81jcPRnChfvdr2GhuClEmDeL16/HLRz/Fxvx3Ue8JDqVfv6jCG5v3AMWbsTKR7SYEXvR8LN15bkrF4rwKNHjq+CZctj0obF+NLQb/o2bCPH740yrxT0+R2osFW1c/jZycJdDF+n79JCYWE+46DOgGOB0ielSZ0ygVENosMOl8j/+SRv6ENtje3Iv2/A0wTPfNtY6fj5U582HdVozyc77Ly+4/4cj+U3h0/RIkMKJRpPbJqAhjf4loEJfyPA7aczGtwoAJnmfSPYiCKyvx293LA55h1l8qXBatAlKQ9wKOlc/DqSUzECvV/4yXceIOI6oqc0P3cjV3InN3Jd5b9Bfk6W5HjHRC1x/F1BcOBT2+IVpdmG9o/h53P3gvmovWIFWqY92zeP/qYyjfZ8Qc2eNqBnP88P5aShaKal29oQ0/wUJ2SHu78JNRFdBMTMSDjzhRJD3+KzYGumc+wNWs3dgXMAViElJy3oW9YAoq7pronX+dWIwrT7+D3Zl3Bj63c1RLE907j5FuZu6vCNJvbN5ilf425zIKDLsA2+jwEdN2+GyZsroF+N1Rd/2qoXSh2ihHDNVQuywDBShAAQpQgAIUUECAgaECiEyCAhSgAAUoQAEKqEGAgaEaapFloAAFKEABClCAAgoIMDBUAJFJUIACFKAABShAATUIMDBUQy2yDBSgAAUoQAEKUEABAQaGCiAyCQpQgAIUoAAFKKAGAQaGaqhFloECFKAABShAAQooIMDAUAFEJkEBClCAAhSgAAXUIHCbGgrBMlBAelAn/4ZHgLbD48pU1S/A747661iNJQwrMGTjVmPVs0wUoAAFKEABClAgUOCWgSF/Di8QjO8iT4Adl8irE+aIAhSgAAWiU4BzDKOz3phrClCAAhSgAAUooLjALUcMFd8jE6TAMAhwZHsYUAFIo7G0HR5bpqpuAX531F2/aihdqKttHDFUQ+2yDBSgAAUoQAEKUEABAQaGCiAyCQpQgAIUoAAFKKAGAQaGaqhFloECFKAABShAAQooIMDAUAFEJkEBClCAAhSgAAXUIMDAUA21yDJQgAIUoAAFKEABBQQYGCqAyCQoQAEKUIACFKCAGgQYGKqhFlkGClCAAhSgAAUooIAAA0MFEJkEBShAAQpQgAIUUIMAA0M11CLLMEwCf4PLssHzkGfpQaAxMRtgcf1Nti8BnbZ86DzLpOWLUdLgli3nSwpQgAIUoEB0CTAwjK76Ym5HVcCOurNXZTn4Gn8+fQou2Sd8SYGBCgiuk9hlTPZ2QBbnw+LoDEyi04Y8ndTxCP6nQ4b5HITAtQPe3TJtz9qdcNiO4kiJEQl5NgTtPSA9vqHA8ArchKt+D4ye9q7D4jwLHG55Cw/ujMu/Eythdly/RfYuw5aXKvsu3fo7dIsEVbmYgaEqq5WFGh6BBlRUf9Fz4hRa8fnx5uHZFVMdGwLuz1FljcWT+xohdjlRt6wNG/VvwtbpPxkK6LR/goo+ex8LsWrhTIQ8iN8ybYn4Ohzml/DP+8vx4pYD+HpsqLOUESkgwP3Hj2BFJvY5RXQ5P8Sy9l9A/0ZtzzEXV2CvtvbdGTf8BAsTxvdbMqHtBN6vaJCtc4vvkGzNsfQy5DFlLCGwrBS4pcDqHOQatHBVfAK776QttPweh6wuaDflImd2cAoC3A4bzHkZvt6p1Ps1wxY8GuR24HiJUXY5OhnGEgsaXDd9Cf4HLMYExMQkwHjkD2iwlPh60zHQGfegvnu94P3zfeQLXMd5+zdYkH0ftNKRWKNFmsmIbFhRbb/iy/4V2E9PxXvOG57frJZ+t9rzr6MGuT/t70QYTtrSLsYjcV0Z3t9XgO0GbeSTMYfqFRAuwd4xH9lpWk9nR6O9HybjUkB2zEVnE07fXgBnl+974Pk+dKGj5lX8dNUDSOg3ormKP35wFFPe+6vsu3QY6xL7DybVCx66ZP0yht6MSygwxgRum4eMVQsB1ymc/rM0rnIdLZ99DCtSkP3oQwg+pQptVdikXwJTkdUH5UJtkQlL9C/BfM53sU64BMumLBi2HJD1gJtwYEsWlm77N7T5B408KZzHgRX3IzVrCw74Ro9cBzZiwdr34AhYb4zVS1QXdzxm6+/DdNlRWGi/iDNJT2Fl2mRvyQQBMx43IV07TlbS63AcKcOZzP5OhGGkLUuRLykw6gKa70Ovv0M2An4T7RcvISlnOdLivV8S4as78HjuEm9Hyp9hwYEjheeR2d/oubRu52kcLj2AojeKYbbUBl2i9ifG/yUB2SGJIBSgQGiBb+MH96ZhNppx/PNWCHCjtfkCgFQsuHtK0GaXUfvWTphdc7GmrBHXPL3aDpwtWwety4xt++yeSyNCSw3eMTcB+lLYr3VBFG+gtfJ5T5Dp+vQC2oMDPv1WVDZ3BKwHaz2a/o/8hpigrPBtlAhI8/zM2LrDhbyDzyMlzndo1nwHibPjA8sgXMRnlqlYnzErzAN4iLQDU+U7CkSOgNsBm/l17GhZi4M5aYjz5UyjnY3Z/u+G7zPpyo1lRhYy+r2MLHWm9qJI6lTXFsGUtRhJS7f1ns8bOQKjmhMGhqPKz51Hk8BtP5iPLK0L1kO/R8vVL1AtzVUxpGHud/9LYDH+dgmnK6V5LE04YErGBM9NAxNxl8nsGRn0X47WJK5DtSii6+CP0WqtgsX8Kp7O2uMdPfz6Cjq+lkeGWhiy12B5ohQkjMP0+9PxSOBe+S5aBTw3l0xE0hITig6cQPWpC+jv3nbPifCHy/DwdPkoYojCDzDtEKnwYwqMkIDv5pIJSVhiKsCBU7/DqZb+boeSrtzU44dP/Thg5L13ZqUpE4c9nWqn/RjKcg1AbQGy1pehIeDmlt5bjsVPGBiOxVpnmQcnEH8PMrJTAOsxWH5tQYVLC0Nf81r+egmN5/vZhesKrn4lAO4mmI3JiNWlYnlWFrJMRaj1b/atyZj4LfnX81uYNunbPSNEU+9Ecq95jf6N+X9UCcSno9Az2b4O5blAUdYKbLJcCnG3se9EmHEPgsYR+y7ygNLuOwl+SoGRE9AgPn0nnOINOO0HkItyZOnzYWnzz7kOyoln9Pw7yEj1Tb0IWtz77ThoUx7DusJjcNb8E/S17+NwvX8+b++1x+on8jPPWDVguSkQpsAk3LUgFUAVtm6RRvZC3NH27UmY5pl0qEex/ZpsorN/wvReZGr/Bsfh12E6IF1KzkVZ5b/D7ryB/7QXg/FemNWhstU02jQYC3ajzPAlPqo73/eo4YBPhF6ksNJWmSeLE80CUgCXjYJ3tsPg+gPqmvseNfSOnuuR6puDGH6Jx0Gb/jxezUXgkybCT0DVazIwVHX1snDKCtyG785Ng8GfqDYBM6f1cTnPP7KIWpS+VYlz0qUKoQ22fO8dyjrPs+L8cxQB7awFyFj+X5Hy3b/iROVx9DfY6N81/1epgGYmFko3OYX4G/yJUJpR3n/aIXbJjykwagKahAewynB7iP0PcPS8VypxmJGUhOQkXfccxl6rjNEPGBiO0YpnsQcn4D1Qee9B1mY/HKKnOhlpz7yANVrAdWAt7poQi5jYGVhSYAW067D9mVTEIx5JC+7z3mhizsKM2BjvOp/ehF5Kvtccw8Hll1tFm4DUYejAowtm93GyGuqJsL+0o82J+R0TAm4nms//CAuS+pg4McjR8x43N1pbkpH3RGLPFJ2ehWP6FQPDMV39LPyABbpHXVKQHXKelwZxc7Kxp7bGO8nZtxPtmlJYa3dh3RzfDSTLX8Gx8lzoPcu10OcegP3Ir/HCI7MBl/xZdgPOJTeIBgHpcUWmVCzOq/A9t/ImXLY9KGxfjS0G+WM7fIXp70ToT6uk3nsJ2v8+3LSjwYt5VLWA0GaBSZeBvP31cEn33UlXWd7ci/b8DTD0caNVf6Pn3rQeQ0mD75eqBBcajv625/mwggv1u0pR+3A29AO+DK3qavAWTuQfBaJcAJCm8fFvOARoOxyq/jQ7xLNl60QtIErO0K4RiyvtorPLvzzw/67mcnFdcZ14LfBj77uui2LluhRR37083LS7xI6arT158ORlhVjW/E1fe+FnAxDgd2cAWNKq1xrFsjVzvd8FQNSuKRYr7U6x76/DN2JzWa5YbP9/fe6kq7VSXKf9ac/yrlaxZqvBl/ZccU3xb8Sa5o4+tx1LH4ZqozESwhiIf1lEFQtIvyHLZjw8FUzb4XFlquoX4HdH/XUc7SUM1UZ5KTnaa5b5pwAFKEABClCAAgoJMDBUCJLJUIACFKAABShAgWgXYGAY7TXI/FOAAhSgAAUoQAGFBBgYKgTJZChAAQpQgAIUoEC0CzAwjPYaZP4pQAEKUIACFKCAQgIMDBWCZDIUoAAFKEABClAg2gUYGEZ7DTL/FKAABShAAQpQQCEBBoYKQTIZClCAAhSgAAUoEO0CDAyjvQaZfwpQgAIUoAAFKKCQAH/5RCFIJjN6AtLT2/lHAQpQgAIUoMDABYJ/Oey2gSfBLSgQWQLBjeD6+CAAAAA6SURBVDqycsfcUIACFKAABaJHgJeSo6eumFMKUIACFKAABSgwrAIMDIeVl4lTgAIUoAAFKECB6BH4/ysgjCYiT5sxAAAAAElFTkSuQmCC"></p>
</div>

<div class="specification">
<p>For each student, the change from the predicted points to the final points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f - p} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>f</mi>
      <mo>−<!-- − --></mo>
      <mi>p</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span> was calculated.</p>
</div>

<div class="specification">
<p>The data for school B is shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>School A also gives each student a score for effort in each subject. This effort score is based&nbsp;on a scale of 1 to 5 where 5 is regarded as outstanding effort.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>It is claimed that the effort put in by a student is an important factor in improving upon their&nbsp;predicted IB points.</p>
</div>

<div class="specification">
<p>A mathematics teacher in school A claims that the comparison between the two schools is not&nbsp;valid because the sample for school B contained mainly girls and that for school A, mainly boys.&nbsp;She believes that girls are likely to show a greater improvement from their predicted points to&nbsp;their final points.</p>
<p>She collects more data from other schools, asking them to class their results into four categories as shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify a test that might have been used to verify the null hypothesis that the predictions from the standardized test can be modelled by a normal distribution.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why comparing only the final IB points of the students from the two schools would not be a valid test for the effectiveness of the two different teaching methods.</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 mean change.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the standard deviation of the changes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use a paired <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>-test to determine whether there is significant evidence that the students in school A have improved their IB points since the start of the course.</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>Use an appropriate test to determine whether there is evidence, at the 5 % significance level, that the students in school B have improved more than those in school A.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why it was important to test that both sets of points were normally distributed.</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>Perform a test on the data from school A to show it is reasonable to assume a linear relationship between effort scores and improvements in IB points. You may assume effort scores follow a normal distribution.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the expected improvement between predicted and final points for an increase of one unit in effort grades, giving your answer to one decimal place.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use an appropriate test to determine whether showing an improvement is independent of gender.</p>
<div class="marks">[6]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If you were to repeat the test performed in part (e) intending to compare the quality of the teaching between the two schools, suggest <strong>two</strong> ways in which you might choose your sample to improve the validity of the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, <em>X</em> kg, of the males of a species of bird may be assumed to be normally distributed with mean 4.8 kg and standard deviation 0.2 kg.</p>
</div>

<div class="specification">
<p>The weights, <em>Y</em> kg, of female birds of the same species may be assumed to be normally distributed with mean 2.7 kg and standard deviation 0.15 kg.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly chosen male bird weighs between 4.75 kg and 4.85 kg.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the weight of a randomly chosen male bird is more than twice the weight of a randomly chosen female bird.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two randomly chosen male birds and three randomly chosen female birds are placed on a weighing machine that has a weight limit of 18 kg. Find the probability that the total weight of these five birds is greater than the weight limit.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Mr Sailor owns a fish farm and he claims that the weights of the fish in one of his lakes have a mean of 550 grams and standard deviation of 8 grams.</p>
<p>Assume that the weights of the fish are normally distributed and that Mr Sailor’s claim&nbsp;is true.</p>
</div>

<div class="specification">
<p>Kathy is suspicious of Mr Sailor’s claim about the mean and standard deviation of the weights of the fish. She collects a random sample of fish from this lake whose weights are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Using these data, test at the 5% significance level the null hypothesis&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_0}\,{\text{:}}\,\mu&nbsp; = 550">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>0</mn>
    </msub>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>:</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>μ<!-- μ --></mi>
  <mo>=</mo>
  <mn>550</mn>
</math></span>&nbsp;against the alternative hypothesis&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_1}\,{\text{:}}\,\mu&nbsp; < 550">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>1</mn>
    </msub>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>:</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>μ<!-- μ --></mi>
  <mo>&lt;</mo>
  <mn>550</mn>
</math></span>, where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ<!-- μ --></mi>
</math></span>&nbsp;grams is the population mean weight.</p>
</div>

<div class="specification">
<p>Kathy decides to use the same fish sample to test at the 5% significance level whether or not there is a positive association between the weights and the lengths of the fish in the lake. The following table shows the lengths of the fish in the sample. The lengths of the fish can be assumed to be normally distributed.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a fish from this lake will have a weight of more than 560 grams.</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>The maximum weight a hand net can hold is 6 kg. Find the probability that a catch of 11 fish can be carried in the hand net.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the distribution of your test statistic, including the parameter.</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 <em>p</em>-value for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion of the test, justifying your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State suitable hypotheses for the test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the product-moment correlation coefficient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <em>p</em>-value and interpret it in this context.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use an appropriate regression line to estimate the weight of a fish with length 360 mm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The times <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>, in minutes, taken by a random sample of 75 workers of a company to travel to work can be summarized as follows</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum {t = 2165} ">
  <mo>∑<!-- ∑ --></mo>
  <mrow>
    <mi>t</mi>
    <mo>=</mo>
    <mn>2165</mn>
  </mrow>
</math></span> ,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum {{t^2} = 76475} ">
  <mo>∑<!-- ∑ --></mo>
  <mrow>
    <mrow>
      <msup>
        <mi>t</mi>
        <mn>2</mn>
      </msup>
    </mrow>
    <mo>=</mo>
    <mn>76475</mn>
  </mrow>
</math></span>.</p>
<p style="text-align: left;">Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
  <mi>T</mi>
</math></span> be the random variable that represents the time taken to travel to work by a worker of this company.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find unbiased estimates of the mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
  <mi>T</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find unbiased estimates of the variance of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
  <mi>T</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assuming that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
  <mi>T</mi>
</math></span> is normally distributed, find</p>
<p>(i)  the 90% confidence interval for the mean time taken to travel to work by the workers of this company,</p>
<p>(ii)  the 95% confidence interval for the mean time taken to travel to work by the workers of this company.</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>Before seeing these results the managing director believed that the mean time was 26 minutes.</p>
<p>Explain whether your answers to part (b) support her belief.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Anne is a farmer who grows and sells pumpkins. Interested in the weights of pumpkins produced, she records the weights of eight pumpkins and obtains the following results in kilograms.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\text{7.7}}\quad {\text{7.5}}\quad {\text{8.4}}\quad {\text{8.8}}\quad {\text{7.3}}\quad {\text{9.0}}\quad {\text{7.8}}\quad {\text{7.6}}">
  <mrow>
    <mtext>7.7</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>7.5</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>8.4</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>8.8</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>7.3</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>9.0</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>7.8</mtext>
  </mrow>
  <mspace width="1em"></mspace>
  <mrow>
    <mtext>7.6</mtext>
  </mrow>
</math></span></p>
<p>Assume that these weights form a random sample from a <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N(\mu ,{\text{ }}{\sigma ^2})">
  <mi>N</mi>
  <mo stretchy="false">(</mo>
  <mi>μ<!-- μ --></mi>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msup>
      <mi>σ<!-- σ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span> distribution.&nbsp;</p>
<p>&nbsp;</p>
</div>

<div class="specification">
<p>Anne claims that the mean pumpkin weight is 7.5 kilograms. In order to test this claim, she sets up the null hypothesis <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{H}}_0}:\mu&nbsp; = 7.5">
  <mrow>
    <msub>
      <mrow>
        <mtext>H</mtext>
      </mrow>
      <mn>0</mn>
    </msub>
  </mrow>
  <mo>:</mo>
  <mi>μ<!-- μ --></mi>
  <mo>=</mo>
  <mn>7.5</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine unbiased estimates for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2}">
  <mrow>
    <msup>
      <mi>σ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use a two-tailed test to determine the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>-value for the above results.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret your <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>-value at the 5% level of significance, justifying your conclusion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A shop sells carrots and broccoli. The weights of carrots can be modelled by a normal&nbsp;distribution with variance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>&nbsp;</mo><msup><mtext>grams</mtext><mn>2</mn></msup></math> and the weights of broccoli can be modelled by a normal&nbsp;distribution with variance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo>&nbsp;</mo><msup><mtext>grams</mtext><mn>2</mn></msup></math>. The shopkeeper claims that the mean weight of carrots&nbsp;is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>130</mn><mo>&nbsp;</mo><mtext>grams</mtext></math> and the mean weight of broccoli is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo>&nbsp;</mo><mtext>grams</mtext></math>.</p>
</div>

<div class="specification">
<p>Dong Wook decides to investigate the shopkeeper’s claim that the mean weight of carrots&nbsp;is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>130</mn><mo>&nbsp;</mo><mtext>grams</mtext></math>. He plans to take a random sample of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> carrots in order to calculate a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>98</mn><mo> </mo><mo>%</mo></math>&nbsp;confidence interval for the population mean weight.</p>
</div>

<div class="specification">
<p>Anjali thinks the mean weight, <math xmlns="http://www.w3.org/1998/Math/MathML"><mpadded lspace="-1px"><mi>μ</mi><mo>&nbsp;</mo><mi>grams</mi></mpadded></math>, of the broccoli is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo>&nbsp;</mo><mtext>grams</mtext></math>. She decides&nbsp;to perform a hypothesis test, using a random sample of size <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>. Her hypotheses are</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mn>0</mn></msub><mo>&nbsp;</mo><mo>:</mo><mo>&nbsp;</mo><mi>μ</mi><mo>=</mo><mn>400</mn><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><msub><mi>H</mi><mn>1</mn></msub><mo>&nbsp;</mo><mo>:</mo><mo>&nbsp;</mo><mi>μ</mi><mo>&lt;</mo><mn>400</mn></math>.</p>
<p>She decides to reject <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mn>0</mn></msub></math> if the sample mean is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>395</mn><mo>&nbsp;</mo><mtext>grams</mtext></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assuming that the shopkeeper’s claim is correct, find the probability that the weight of six randomly chosen carrots is more than two times the weight of one randomly chosen broccoli.</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>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> required to ensure that the width of the confidence interval is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mtext>grams</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the significance level for this test.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the weights of the broccoli actually follow a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>392</mn><mo> </mo><mtext>grams</mtext></math> and variance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo> </mo><msup><mtext>grams</mtext><mn>2</mn></msup></math>, find the probability of Anjali making a Type II error.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two independent random variables <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y">
  <mi>Y</mi>
</math></span> follow Poisson distributions.</p>
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right) = 3">
  <mrow>
    <mtext>E</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mi>X</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left(&nbsp;Y \right) = 4">
  <mrow>
    <mtext>E</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mi>Y</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>4</mn>
</math></span>, calculate</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( {2X + 7Y} \right)">
  <mrow>
    <mtext>E</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>2</mn>
      <mi>X</mi>
      <mo>+</mo>
      <mn>7</mn>
      <mi>Y</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Var<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {4X - 3Y} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>4</mn>
      <mi>X</mi>
      <mo>−</mo>
      <mn>3</mn>
      <mi>Y</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( {{X^2} - {Y^2}} \right)">
  <mrow>
    <mtext>E</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <msup>
          <mi>X</mi>
          <mn>2</mn>
        </msup>
      </mrow>
      <mo>−</mo>
      <mrow>
        <msup>
          <mi>Y</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question is about modelling the spread of a computer virus to predict the number of computers in a city which will be infected by the virus.</strong></p>
<p><br>A systems analyst defines the following variables in a model:</p>
<ul>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>&nbsp;is the number of days since the first computer was infected by the virus.</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> is the total number of computers that have been infected up to and&nbsp;including day <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</li>
</ul>
<p>The following data were collected:</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>A model for the early stage of the spread of the computer virus suggests that</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>&#946;</mi><mi>N</mi><mi>Q</mi><mfenced><mi>t</mi></mfenced></math></p>
<p style="text-align: left;">where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> is the total number of computers in a city and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#946;</mi></math> is a measure of how easily the virus is spreading between computers. Both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#946;</mi></math> are assumed to be constant.</p>
</div>

<div class="specification">
<p>The data above are taken from city X which is estimated to have <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>6</mn></math> million computers.<br>The analyst looks at data for another city, Y. These data indicate a value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#946;</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>64</mn><mo>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>8</mn></mrow></msup></math>.</p>
</div>

<div class="specification">
<p>An estimate for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>&#8242;</mo><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mo>&#160;</mo><mi>t</mi><mo>&#8805;</mo><mn>5</mn></math>, can be found by using the formula:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>&#8776;</mo><mfrac><mrow><mi>Q</mi><mfenced><mrow><mi>t</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>-</mo><mi>Q</mi><mfenced><mrow><mi>t</mi><mo>-</mo><mn>5</mn></mrow></mfenced></mrow><mn>10</mn></mfrac></math>.</p>
<p>The following table shows estimates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>'</mo><mo>(</mo><mi>t</mi><mo>)</mo></math> for city X at different values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>An improved model for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>, which is valid for large values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is the logistic&nbsp;differential equation</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>k</mi><mi>Q</mi><mfenced><mi>t</mi></mfenced><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>Q</mi><mfenced><mi>t</mi></mfenced></mrow><mi>L</mi></mfrac></mrow></mfenced></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> are constants.</p>
<p>Based on this differential equation, the graph of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Q</mi><mo>'</mo><mfenced><mi>t</mi></mfenced></mrow><mrow><mi>Q</mi><mfenced><mi>t</mi></mfenced></mrow></mfrac></math>&nbsp;against&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>&nbsp;is predicted to be&nbsp;a straight line.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, Pearson’s product-moment correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why it would not be appropriate to conduct a hypothesis test on the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> found in (a)(ii).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the general solution of the differential equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>β</mi><mi>N</mi><mi>Q</mi><mfenced><mi>t</mi></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the data in the table write down the equation for an appropriate non-linear regression model.</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 value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mn>2</mn></msup></math> for this model.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence comment on the suitability of the model from (b)(ii) in comparison with the linear model found in part (a).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By considering large values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> write down one criticism of the model found in (b)(ii).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer from part (b)(ii) to estimate the time taken for the number of infected computers to double.</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 in which city, X or Y, the computer virus is spreading more easily. Justify your answer using your results from part (b).</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>Determine the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>. Give your answers correct to one decimal place.</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>Use linear regression to estimate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The solution to the differential equation is given by</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mfrac><mi>L</mi><mrow><mn>1</mn><mo>+</mo><mi>C</mi><msup><mtext>e</mtext><mrow><mo>-</mo><mi>k</mi><mi>t</mi></mrow></msup></mrow></mfrac></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is a constant.</p>
<p>Using your answer to part (f)(i), estimate the percentage of computers in city X that are expected to have been infected by the virus over a long period of time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>In a large population of hens, the weight of a hen is normally distributed with mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ<!-- μ --></mi>
</math></span> kg&nbsp;and standard deviation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
  <mi>σ<!-- σ --></mi>
</math></span> kg. A random sample of 100 hens is taken from the population.</p>
<p>The mean weight for the sample is denoted by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar X">
  <mrow>
    <mover>
      <mi>X</mi>
      <mo stretchy="false">¯<!-- ¯ --></mo>
    </mover>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The sample values are summarized by&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum {x = 199.8} ">
  <mo>∑<!-- ∑ --></mo>
  <mrow>
    <mi>x</mi>
    <mo>=</mo>
    <mn>199.8</mn>
  </mrow>
</math></span> and&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum {{x^2} = 407.8} ">
  <mo>∑<!-- ∑ --></mo>
  <mrow>
    <mrow>
      <msup>
        <mi>x</mi>
        <mn>2</mn>
      </msup>
    </mrow>
    <mo>=</mo>
    <mn>407.8</mn>
  </mrow>
</math></span>&nbsp;where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> kg is the weight of a hen.</p>
</div>

<div class="specification">
<p>It is found that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
  <mi>σ<!-- σ --></mi>
</math></span> = 0.27 . It is decided to test, at the 1 % level of significance, the null hypothesis <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ<!-- μ --></mi>
</math></span> = 1.95 against the alternative hypothesis <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu&nbsp;">
  <mi>μ<!-- μ --></mi>
</math></span> &gt; 1.95.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the distribution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar X">
  <mrow>
    <mover>
      <mi>X</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span> giving its mean and variance.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an unbiased estimate for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an unbiased estimate for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2}">
  <mrow>
    <msup>
      <mi>σ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a 90 % confidence interval for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>-value for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the conclusion reached.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>John rings a church bell 120 times. The time interval, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_i}">
  <mrow>
    <msub>
      <mi>T</mi>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span>, between two successive rings is a random variable with mean of 2 seconds and variance of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{9}{\text{ second}}{{\text{s}}^2}">
  <mfrac>
    <mn>1</mn>
    <mn>9</mn>
  </mfrac>
  <mrow>
    <mtext>&nbsp;second</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
<p>Each time interval, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_i}">
  <mrow>
    <msub>
      <mi>T</mi>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span>, is independent of the other time intervals. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X = \sum\limits_{i = 1}^{119} {{T_i}} ">
  <mi>X</mi>
  <mo>=</mo>
  <munderover>
    <mo movablelimits="false">∑<!-- ∑ --></mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mn>119</mn>
    </mrow>
  </munderover>
  <mrow>
    <mrow>
      <msub>
        <mi>T</mi>
        <mi>i</mi>
      </msub>
    </mrow>
  </mrow>
</math></span> be the total time between the first ring and the last ring.</p>
</div>

<div class="specification">
<p>The church vicar subsequently becomes suspicious that John has stopped coming to ring the bell and that he is letting his friend Ray do it. When Ray rings the bell the time interval,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_i}">
  <mrow>
    <msub>
      <mi>T</mi>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span> has a mean of 2 seconds and variance of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{25}}{\text{ second}}{{\text{s}}^2}">
  <mfrac>
    <mn>1</mn>
    <mrow>
      <mn>25</mn>
    </mrow>
  </mfrac>
  <mrow>
    <mtext>&nbsp;second</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
<p>The church vicar makes the following hypotheses:</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_0}">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math></span>: Ray is ringing the bell; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_1}">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>: John is ringing the bell.</p>
<p>He records four values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>. He decides on the following decision rule:</p>
<p>If <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="236 \leqslant X \leqslant 240">
  <mn>236</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>X</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>240</mn>
</math></span> for all four values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> he accepts <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_0}">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math></span>, otherwise he accepts <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_1}">
  <mrow>
    <msub>
      <mi>H</mi>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find</p>
<p>(i) &nbsp; &nbsp; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X)">
  <mrow>
    <mtext>E</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mo stretchy="false">)</mo>
</math></span>;</p>
<p>(ii) &nbsp; &nbsp; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X)">
  <mrow>
    <mtext>Var</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why a normal distribution can be used to give an approximate model for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this model to find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
  <mi>A</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(A < X < B) = 0.9">
  <mrow>
    <mtext>P</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>A</mi>
  <mo>&lt;</mo>
  <mi>X</mi>
  <mo>&lt;</mo>
  <mi>B</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>0.9</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
  <mi>A</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span> are symmetrical about the mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that he makes a Type II error.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An estate manager is responsible for stocking a small lake with fish. He begins by introducing <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> fish into the lake and monitors their population growth to determine the likely carrying capacity of the lake.</p>
<p>After one year an accurate assessment of the number of fish in the lake is taken and it is found to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1200</mn></math>.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> be the number of fish <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> years after the fish have been introduced to the lake.</p>
<p>Initially it is assumed that the rate of increase of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> will be constant.</p>
</div>

<div class="specification">
<p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>8</mn></math> the estate manager again decides to estimate the number of fish in the lake. To do this he first catches <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math> fish and marks them, so they can be recognized if caught again. These fish are then released back into the lake. A few days later he catches another <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math> fish, releasing each fish after it has been checked, and finds <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> of them are marked.</p>
</div>

<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> be the number of marked fish caught in the second sample, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> is considered to be distributed as <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mfenced><mrow><mi>n</mi><mo>,</mo><mo> </mo><mi>p</mi></mrow></mfenced></math>. Assume the number of fish in the lake is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2000</mn></math>.</p>
</div>

<div class="specification">
<p>The estate manager decides that he needs bounds for the total number of fish in the lake.</p>
</div>

<div class="specification">
<p>The estate manager feels confident that the proportion of marked fish in the lake will be within <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> standard deviations of the proportion of marked fish in the sample and decides these will form the upper and lower bounds of his estimate.</p>
</div>

<div class="specification">
<p>The estate manager now believes the population of fish will follow the logistic model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mfrac><mi>L</mi><mrow><mn>1</mn><mo>+</mo><mi>C</mi><msup><mi>e</mi><mrow><mo>-</mo><mi>k</mi><mi>t</mi></mrow></msup></mrow></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is the carrying capacity and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>,</mo><mo> </mo><mi>k</mi><mo>&gt;</mo><mn>0</mn></math>.</p>
<p>The estate manager would like to know if the population of fish in the lake will eventually reach <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5000</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this model to predict the number of fish in the lake when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>8</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assuming the proportion of marked fish in the second sample is equal to the proportion of marked fish in the lake, show that the estate manager will estimate there are now <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2000</mn></math> fish in the lake.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State an assumption that is being made for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> to be considered as following a binomial distribution.</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>Show that an estimate for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Var</mtext><mo>(</mo><mi>X</mi><mo>)</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38</mn><mo>.</mo><mn>25</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence show that the variance of the proportion of marked fish in the sample, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Var</mtext><mfenced><mfrac><mi>X</mi><mn>300</mn></mfrac></mfenced></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>000425</mn></math>.</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>Taking the value for the variance given in (d) (ii) as a good approximation for the true variance, find the upper and lower bounds for the proportion of marked fish in the lake.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find upper and lower bounds for the number of fish in the lake when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>8</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given this result, comment on the validity of the linear model used in part (a).</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>Assuming a carrying capacity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5000</mn></math> use the given values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mn>0</mn></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mn>1</mn></mfenced></math> to calculate the parameters <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use these parameters to calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mn>8</mn></mfenced></math> predicted by this model.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the likelihood of the fish population reaching <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5000</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Peter, the Principal of a college, believes that there is an association between the score in a&nbsp;Mathematics test, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>, and the time taken to run 500 m, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y">
  <mi>Y</mi>
</math></span> seconds, of his students.&nbsp;The following paired data are collected.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAd4AAAA3CAYAAACiois9AAAYNElEQVR4Ae2d7Y0tu3FFlYehBAwlYCgCKwIrAisCKwIrAysCKwIrAisCK4OXgTK4xnrAethTKHaTfXpmTgMk0GA3WazateuDZ37Nr37ssRnYDGwGNgObgc3AlzHwqy+ztA1tBjYDm4HNwGZgM/BjX7w7CTYDm4HNwGZgM/CFDHy4eH/963/6sZ/Nwc6BnQM7B3YO7By4NwfyXv9w8bIB2XtsBjYDn8PAU+rrKTiJ0lOwbpz319RTOd0X7/25sDVuBoYMPLVRDB16g43N6b1BeAqfeP0UrBXnvnjvzdmtbTNwyEAtwEPhb9x8Ck4oegrWjfP+hH4qp/vivT8XtsbNwJCBpzaKoUNvsLE5vTcIT+ETr5+CteLcF++9Obu1bQYOGagFeCj8jZtPwQlFT8G6cd6f0E/ldF+89+fC1rgZGDLw1EYxdOgNNjan9wbhKXzi9VOwVpxLF+8f/vDvPzuKkr///f/aaP/2t//ys8yf//xf7f5oEX1/+tN//rLNO3b+8Y9//LL2ji9/+ct//0hff/e7f/3B85mj2rzL1mfpvQvfHXr++Mf/+CWHyS9j9dNPP31YP8rxV3Cg98qouNHD85vf/PMHdcSQNfZ+//t/u1w/V3FiX2x1/tvf/vcDVrhPGfrLlXEVq70qMfAOb92gzsWcvaqT7dau4kxdf/3r//yMD13mbu7zPiNTz+T3HTipp8zZ7OP0enlkHt0liWn0fgfWo7iyRz5czU1xV5zLFy9FzZOXjcopLJO521eumwlAJtITLl6SCUKvFGHHwczaZ9n8LL0zPn21DLlJ3GgMOVgntz8znrUA0/7Ru5cp5/PJS8JL10ZGs8iaOtJf967iBE/i8x38OegV7jmD/8rg/Oro7Iuj9i5qA79ezY0rONMvLzJmLrZuzMh053LtVZz++IIzfgTkADc8yrE1N/Inz3bvr2A9iytcWndvcfFCKE8dAPXClNgqM/reF++ImY/rn3VBfpbej+jf54uC4nHQiMnBqw1APWfzlUZB86K26gBvXlb86M0fDcQ0m1w9f/R9BaeNjDkHmCp+Gtlqj0id+X4FK5iSO/TJV80BeKbfVb8Sw8z7FZzqhT/i648q13OekUn50fsrOL10K7fa6n4Mwu/Vi+0VrLNxpYau4tPvivPSX7ySWxMUgP6SzKJCjsTFuE/uQ4DrzCRXXuDukXg1oBQDpCiDrvyVxTt72POvcXCih8e1Lqk5m9jSPna1yYxOBvI8joovdSCTGNADT6PiGtlED2eSY94zPhWHnHD2SK9+OM/ghevkJmONnowFcrUpE3s41B+59ay6Wa+6xXk2YxM98OalCw+fPbC5OsBXB7FNXqy7KguHPKvjCk4wdRyS84kLztEPfmLdnVnBewVr4tEWuV258jJ7FSM2ruDkHLg422FO7Gcyyp7NV3Gak0c12dUs8pnLZ/hy/yrWlbiC7S0uXgjGYRLCwSVFgZGg7CX5rCdw9ur5emF58VIIJj3vnMO+w3Ouec4k9eIFgzLq4ay6eUfGYXNIP7zg1aOv2HSIJ7/TtjrQr408D7bEoR7nziZ4SA7OOtSjf9hNHPKif51edTnP4JV/9DOMtXb8NnfQCa7Erg4vZGPJN36qu/ogzpnZs9jNPJg5+4oM+XvHgEf5QZ+8mpvakDO/Z+e7cBK7ms9gQr9PxnQWX8rdhZVcMC/Rb75TO+xhB6wpkzjO3q/ihD9y1N6BnuwZ2J2ROcPn/lWc4IMf6xc98GYPIhdYq/zxzbp1Lo6Z+QrW1bjiE769MirOS3/xAgBCeRwUE8VvA+edIak461AmG0e9sAxeBsPA2XjVnTLYIAklygYrHvZtUpkArpkkYKsNQ12e048sgvRDvGlbDpjVV/GnTH3vbIKV5MhBAybY2gZXxitlee/0VpkZvOA4ssN+xh0b6mVmGPvMmeqP2Lo4uXc06y94eP+qUQvwql1yU77QIWfVl9H6md27cBKfrI+0S26SK9h6JQ53YPXHa/JnT7CG2BNvcp8+Hb1fwWkPoZ+JDU7RJa8zMke46t4VnOiw9q1b+zO9h1HrXLujdfeP5itYV+OKX94nR1iO9irOyxcv4AHk4B3CSQ6MmKzuEwQShYemgUw6kxcWZ5BDxmRjDf2pmwRMDNrK9S6oEm+CcK5bc13c2E77+sq+I/1Q5+hi5Tz44QMd9a8Vdebc2eR8cql8rssncjU2yHd61eN8htcG0OlHh/v+cEm98CqPYsWewyLOmLE3WvfcaBYLdtPOSP6udey9OuCA2OboOGN/tJ5nu/c7cKIXnDVm1Z4YR3lT5ev3HVixXWuI79pf/AF49OOy4vP7Ck5wca72EHgV24yMGGbmKziJMedqDP2RAP6uF4NntP5ZWFfjCs81N2awpUzl9PLFK9GQRvPzV40N3ADwzR6GSVaKzKaXzuSFBWCLMZuiNtXNefSOHs52QTVRsyHUNfYgHN0kD3hs8trXV/Yc6Yc+pB3lnClk5bCFTfUrk3NnU5wdD8YFHej1FzuyvHvZd3rTru9HeOV6hN995jrwQR7lA0wOdHb+udbp9GydyT940c7K2apr9Ru8rw5wy5W65Md4up4/Ql2bme/ACa+Zf0d2kct+cCRb9+7Aiv2aB+AhL+vg0pv1K89ewWlcaw/xQqNGZmQSx9n7FZzg4xxYctgz4da+z1oOZdhfHVewrsaVHLiam/pTcV6+eFFIApIAgJJwG7jfzADPhqBMOkMiZzLbFLP51uBiGwxHg4DjdBYVmFjLZK5rXEqJBxvq0jf9yCaYfqhzNqHA48VYk1MfO5vGQZmZGWzERf46vWd6Kl4LS37qeferb9V2F3uLM/Oo6p/5BgM+Y9N8yvjN6HhFphbgFV3grzklt3WdfOJZHXfgpD5HuVDxEIOrcXgVKznVXbDg79ap8a/i1LyvcYUrsc3IVL6Pvq/wCYecq/G2Z4ofzFWGb305wtXtXcG6Glew5V3V4ThbqzhfungJPk0AYDZEm6jkAriSapNIZ3jPiw7dgEWfw0apbmZkWM9BUajLwK9evB3Z2tM+NpHLhpEXr36mfOLs3it/nUy1CXdeoClf5XKP9yxevs/k63m+K150HDUl9kn8HMbIC3km9p6HW3RmnrhXZ/QTH3OVfc523NWzd33XAlzVS06N8LKeuQgn+LeSf+J5FSd6sJ1cq7ubiUut406uW3sVK/zUnMROzUttw/NXcWoMKz6+rbMZGbHPzFf5JIY1N6k58sBR+zzrnMu7QNmZ+QrW1biC/yo+fag4X7p4vVggzkESYMTEZObbi4/iQp61dIZ3g4aO2eaLLh4LvNqTZO2DU5ks9LomHvWaQOkbuggKRaCceOSD4sAv97XDjE70MTv0O7G551xtops1CxE53lmDSwYYWPObM6xlDKpe7TnP4NU/+cYP9GrHfX1mHxzw5pADsboOz+hSNzPfedkomzO+Godc5531GoMqc+c3tl4ZcACH3YBT+DB38C157c6M1l7FCRbsd4N4iZF9cmPkU3e+rr2Klfyjl3XDvBEv/H81p7VmjLM9BdwzMp1/3dpVPr0P4IhhbVvrrNmrjDczOZu+dJhGa1exrsQVfPavEY6z9YrzpYsXYyStJPJNs8RIrhEI1niU13EBEyQcRIaG2jVfZKpu7EFK6s9Ao0ud2gIbaxYT63UNvWBUL+82ehMrzyHHmXrxIlPxJTe86zc6OI+doyFWbSKLLxVv+ufloz/M6Qc6Or0Vxwze1IOdejGyTx6IpeLoYi+Oqpvvo1Hl01byLpYjXXfsYeeVAW9HTcqmjB3yjpy8Ml7Fie2sw8RQ8/Qs3/Ns9/4KVmoETo9G1i/Yv4PTzGN6RNa22GdklD2aX+GTWFrb1FeXA2DHB+zAZ+fLEb7cewXrWVyTT+zw3BX7pYs3Hd7vm4HNwDoDrzSKdWvXTzwFJx4+BevGeT0fRyefyum+eEcR3eubgU9g4KmN4hOouE3l5vQ2Kn9W9BQ+AfsUrBXnvnjvzdmtbTNwyEAtwEPhb9x8Ck4oegrWjfP+hH4qp/vivT8XtsbNwJCBpzaKoUNvsLE5vTcIT+ETr5+CteLcF++9Obu1bQYOGagFeCj8jZtPwQlFT8G6cd6f0E/ldF+89+fC1rgZGDLw1EYxdOgNNjan9wbhKXzi9VOwVpwfLl4297M52Dmwc2DnwM6BnQP35kD+PPpw8T7pF0Q6sd83A09hgGb2hPEUnHD5FKwb5/2Z/1RO98V7fy5sjZuBIQNPbRRDh95gY3N6bxCewidePwVrxbkv3ntzdmvbDBwyUAvwUPgbN5+CE4qegnXjvD+hn8rpvnjvz4WtcTMwZOCpjWLo0BtsbE7vDcJT+MTrp2CtOPfFe2/Obm2bgUMGagEeCn/j5lNwQtFTsG6c9yf0UzndF+/9ubA1bgaGDDy1UQwdeoONzem9QXgKn3j9FKwV5/TF2/2nBpTlw3+cOPrPMvemR68NnKv/7QTcPN8x+G8Xr/wXme/AXG36n0bMBfzJkf+NBNnuv5Hkf9V55T/ApN3Zd/JF7M78ByAw+c2c/9loVneVQ8/sIJfhovLpeXKHfXSO/hPMjIz6cl7BCU9gBMNo2BfQW/9blWe6OHS5orzzClbPMNf/2DWKb2LH1tl/M0ob+b6C847Yw6e1SWzQOTNWcFZ92OA8z8gmMuwhA77Vfp02Z7FSB8SR2I14mOlB5KP5MJObYq04py9eFTifFZpyXzlbuKuBJPg83zEMIonxxOH/4CSxfEhgB80tC9Ciy39tZ8KbyOTWV8cD2+Cvds2p9Enfrsy1AEc6uARsTqOLF6zugR/5inNGpsMwi9PYIY/9buALOMhxHt67S84fEejimb3gZrEmNnCgn/pjwB/f8pmyxkFcHfaUH73P4rwj9talvZA4YX906STmWZx5hnd7mTbNybTJOzxb//iKPWSvjFms2DSOiUeb5rE4uh5kL8PmKuaKc1+8P3783AhoBt8xTNanXrwkaJfIctklcF4GyGUD5BsuKJIjveq/cwZrXh4UGthG/yT9iu1agGc6wAOuOuCGvcwbcgm8jhkZZeu8ipNLM7lTH40MXTZj1v0xY5NjjffE7vmZeRUrOuGm2vNyyngj1/E/g6vKrOJ8JfbEo/5A8EKvuOr3Kk7Pw2fto3AHFgc+wXMOzqVM7p29r2D1xwgxrQMM/ghj76gHcR67mb9VX/2uOG+/eOtFYpMlABjngWRA51pNEoDrIGcIWEeYDlrM2shi4Rzn3dO+Z8GYCWMBpj3wci51+KsNPdrnDLqUSx3ac5arTjb3znxP+3lOTKzlgBt0OoyRvz7Bg6/pn7I5wwmy6MJGXgLKddiNBzIWQzY71rHP85UDXPhjQcHLUfyuYEP/yoC/zGXPdvxULmdk1FfnVZw1p9SXsXaNueYF57EJ5tqY81z3vooVHdjJmmeN/EVX9iIasmvmRYdhZm0V5yux52yte/vBGb+rOPUdTrGbfYA1cZif4MjBPjbP+k2e8X0Fq/2q1rS4ZntQ7RNiOZorzi+5eDFayWdNArzoMiH8dWaQTBrPdE4q4xlkkCcZLBqSgoKjoBx8W4TqEC8yJAQ6SCIH7+gwyTzHmrZMqMTjeWdl1MO6utUjPzO+6wdJhM7kXpu1SXIGORsO/uKHujxX57yoOQ9H6asJnXFFh/6wj0+crUVn/NMm/sgX8vDEWTmHL9fAXnWmru6d8+jDB+x0F153bmUN/SsDTjscrBsv9eEv+s2TGRnP1nkVZ80p9ZnLfjsTM/YY4samj3vKH82rWNFFfnT5nXybp2JiltsjPKO9VZyJJXWexXVU9+b3mQ+rOMUmX9YedjKO9sjsEZxFDpv2O/XNzCtYR/5rv/aLrgddxVtxfsnFS5HlIHG6NZodw0KsCQIR9Vzq7QKLfG1c2bw5bxESGLCJQ91dACpGbSfmUQGol1ksyDJGlxVyYFMudfC+Yr82SfxHd46KK/fqOz5TYCRXYhQTc45cH9np1rWBHS8d4oBNfOAMwzVl0vbZu7rImxHXZzqO9msBHsmyB56av6O8yvV8Txuj9ZThfRVnzSn1WVt+O3frxI0Y4jP2jadnRvMqVvSYS9jM0fFNvpJL2OGp+Zznj95XcXZYRvGr65ytvdLekj2qw7uKM3WgW55q3mq/1qVnvuvi7XoNPo3Wr+CtnH7JxUuR5egSKtf85VQDMVpXdzZ015hJSkjkIRlMDPWDjyQFA08d3eWNTK6PbKOvJlrqr8E1qLUhjPSrq9uvxahsbZJdExzhUEc36wtnGR2muu4ZsOYYrdsAU54mWuPW+ZT6R++cIz/MjZHc1fVagGd68Ks2sFFccz3f08ZoPWV4X8VZc0p9oziM1jlH7luP6jmaV7Giy9wkdxzmvPnrunN3xr2ZeRXn1diDxfphZhB3ex8X4NFYxZm64Ag7xA89lUvrCzkGddbVb+o8el/Biq0Ok1zBUY7Runmy0iMqzre8eHUMsN1j0JIk3i2M3FcXSQyRfEuoxJkM/gpGJgdnOxyscXZkm/WueFK3WAx6/VbWpEnf3GPufB812dokuyYob3KUto7e0YV+hr9w+cGUwx9Q7Gun/tDggoW7Ojp+qj+c6Xyquuq3fIm/7t/xTc6sjFH+sF5/0MEh+s3fGZkRllWcXQzQTU3RhOtgLS+9um8+z+TfKlZtkYdwxHmwmFtHNpHhzJWxihM7XS7OxlV/sIseni4W1ZdVnJ4nZqm/66fUmOvYIVc50/mp3qN5Bas91PpQ72oPUv4oT9TtXHG+5cVrY67NWCdGs8XK7OiS1ISUOJq0CUMCcMaLED3s1SanfufONnuj4vGcWLRnUKvvI/3q6fa9SLCRg8QHl6O7pMQhR8qezdhKe9hBVw6+te/lXH+Fg5GnjsoX+8YsZTufcr97N+8q3k726lotwDM9o/zp+KlczsiM7K/i7GKA7ox12uryIvfNXesi9+r7KtZ63m9yZqbOkbsyVnG+EvuKDx7RR46fjVWc6uv6JDmI3dGgb7Ff+91Ivq6vYB1dvLVutNHVD3vkNHZXemPF+ZYX74ggi3hUjJ4jmAy/ayOF0CQum7QJmr/AePdiNijMJIyXTHfxKZO68jzvBlGfTIJaIF44owQ9sl+bCb5kMaT/4hPXSnJxFl15Bt9ro+I7OQGPPKLDGNS4sScP8sUautIfcVS7rB8N9JAXqftI/speLcAzHfiVXCkPN+wlVrjJPJ2RUV+dV3F2MUCnNWhNsmauZp5U+8h0flc5vlexdjqoEfIl+ezk4LjLy062rq3ifCX2aRuf6HmfySc28K/2GnMw8fhO/MnXq3yiZ4VTc7Gzt9KDOI/do/zVR+eK8y0vXsASQBLPgmXmOxu0TjlLLJeWFxSEknQOG3cSR8Flk5ZY/wpDF7ZTD++sWag2E/FqD5mjhNcWNsSMbnAbWP8Sq0mtDeaRffxCl7rRge/gclT/WReXGJTNGS5zHz85l0PuXGfGtniQxT/W1IX/GY/Uhw3w53lk0x/k8ZlndviDZ2R3Vs+ZXC3AM3n8GuUPWN2zPuoPthmZDsMqTuuh00XOgYNaIW68Zy6D3fzgPN/os7Y6nbm2ijXPYhdbnT32kk++5Tt1zL6v4nw19uCiRqmD5PsM7ypO9cENmIkfg/jVWLNODtiHk1/1rMwrWK3xzDVtrfQgzmPXfqWOo7nifNuLFyd0ENA8HWHVWYKPLAFnQA6Jpw72IZlvg46s8urjTK6hh+JUD+9JPMnGnkmnnqPiQcbk5CzJ6DAxWUfHme8j+yR54qYALRBtdf7LffqovHPq5b36rhw6sIEvlTdlTHxkwNc1XXUgw4M9uPGb2eLKtU6XdpmrDs7mxZ6yr76je2bI/5Ef+GUMyFfzOfXPyKS877M4iW1i5L3Lg8znmsvmLmeJRdaBeI7mWaypQzzkVMWjnDLoP5JT/myexXlH7K2Vo7oc4Z3F2Z2nv3DeJ7klF11H7o4am8XqvaB9+KljpgfVXjGbqxXn5Yu3gt7fm4HNwDkDtQDPT3yPxFNwws5TsG6c9+fyUzndF+/9ubA1bgaGDDy1UQwdeoONzem9QXgKn3j9FKwV5754783ZrW0zcMhALcBD4W/cfApOKHoK1o3z/oR+Kqf74r0/F7bGzcCQgac2iqFDb7CxOb03CE/hE6+fgrXi3BfvvTm7tW0GDhmoBXgo/I2bT8EJRU/BunHen9BP5fTDxYsT+9kc7BzYObBzYOfAzoF7cyB/dny4eHNjv28GNgObgc3AZmAzcD8D++K9n9OtcTOwGdgMbAY2A0MG/h9fxftPl1/IPwAAAABJRU5ErkJggg=="></p>
<p>It can be assumed that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {X{\text{, }}Y} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>X</mi>
      <mrow>
        <mtext>,&nbsp;</mtext>
      </mrow>
      <mi>Y</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span> follow a bivariate normal distribution with product moment&nbsp;correlation coefficient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho ">
  <mi>ρ<!-- ρ --></mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State suitable hypotheses <span class="mjpage"><math alttext="{H_0}" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </math></span> and <span class="mjpage"><math alttext="{H_1}" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </math></span> to test Peter’s claim, using a two-tailed test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Carry out a suitable test at the 5 % significance level. With reference to the <span class="mjpage"><math alttext="p" xmlns="http://www.w3.org/1998/Math/MathML"> <mi>p</mi> </math></span>-value, state your conclusion in the context of Peter’s claim.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Peter uses the regression line of <span class="mjpage"><math alttext="y" xmlns="http://www.w3.org/1998/Math/MathML"> <mi>y</mi> </math></span> on <span class="mjpage"><math alttext="x" xmlns="http://www.w3.org/1998/Math/MathML"> <mi>x</mi> </math></span> as <span class="mjpage"><math alttext="y = 0.248x + 83.0" xmlns="http://www.w3.org/1998/Math/MathML"> <mi>y</mi> <mo>=</mo> <mn>0.248</mn> <mi>x</mi> <mo>+</mo> <mn>83.0</mn> </math></span> and calculates that a student with a Mathematics test score of 73 will have a running time of 101 seconds. Comment on the validity of his calculation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Employees answer the telephone in a customer relations department. The time taken for an employee to deal with a customer is a random variable which can be modelled by a normal distribution with mean 150 seconds and standard deviation 45 seconds.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the time taken for a randomly chosen customer to be dealt with by an employee is greater than 180 seconds.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the time taken by an employee to deal with a queue of three customers is less than nine minutes.</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>At the start of the day, one employee, Amanda, has a queue of four customers. A second employee, Brian, has a queue of three customers. You may assume they work independently.</p>
<p>Find the probability that Amanda’s queue will be dealt with before Brian’s queue.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question compares possible designs for a new computer network between&nbsp;multiple school buildings, and whether they meet specific requirements.</strong></p>
<p><br>A school&rsquo;s administration team decides to install new fibre-optic internet cables underground.&nbsp;The school has eight buildings that need to be connected by these cables. A map of the&nbsp;school is shown below, with the internet access point of each building labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A&#8211;H</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Jonas is planning where to install the underground cables. He begins by determining the&nbsp;distances, in metres, between the underground access points in each of the buildings.</p>
<p>He finds&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext><mo>=</mo><mn>89</mn><mo>.</mo><mn>2</mn><mo>&#8202;</mo><mtext>m</mtext></math>,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DF</mtext><mo>=</mo><mn>104</mn><mo>.</mo><mn>9</mn><mo>&#8202;</mo><mtext>m</mtext></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>D</mtext><mo>^</mo></mover><mtext>F</mtext><mo>=</mo><mn>83</mn><mo>&#176;</mo></math>.</p>
</div>

<div class="specification">
<p>The cost for installing the cable directly between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>21</mn><mo>&#8202;</mo><mn>310</mn></math>.</p>
</div>

<div class="specification">
<p>Jonas estimates that it will cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>110</mn></math> per metre to install the cables between all the&nbsp;other buildings.</p>
</div>

<div class="specification">
<p>Jonas creates the following graph, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, using the cost of installing the cables between two&nbsp;buildings as the weight of each edge.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The computer network could be designed such that each building is directly connected to at&nbsp;least one other building and hence all buildings are indirectly connected.</p>
</div>

<div class="specification">
<p>The computer network fails if any part of it becomes unreachable from any other part.&nbsp;To help protect the network from failing, every building could be connected to at least&nbsp;two other buildings. In this way if one connection breaks, the building is still part of the&nbsp;computer network. Jonas can achieve this by finding a Hamiltonian cycle within the graph.</p>
</div>

<div class="specification">
<p>After more research, Jonas decides to install the cables as shown in the diagram below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Each individual cable is installed such that each end of the cable is connected to a building&rsquo;s access point. The connection between each end of a cable and an access point has a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>4</mn><mo>%</mo></math> probability of failing after a power surge.</p>
<p>For the network to be successful, each building in the network must be able to communicate with every other building in the network. In other words, there must be a path that connects any two buildings in the network. Jonas would like the network to have less than a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> probability of failing to operate after a power surge.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost per metre of installing this cable.</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>State why the cost for installing the cable between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> would be higher than between the other buildings.</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>By using Kruskal’s algorithm, find the minimum spanning tree for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, showing clearly the order in which edges are added.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the minimum installation cost for the cables that would allow all the buildings to be part of the computer network.</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 why a path that forms a Hamiltonian cycle does not always form an Eulerian circuit.</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>Starting at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, use the nearest neighbour algorithm to find the upper bound for the installation cost of a computer network in the form of a Hamiltonian cycle.</p>
<p><strong>Note:</strong> Although the graph is not complete, in this instance it is not necessary to form a table of least distances.</p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By deleting <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, use the deleted vertex algorithm to find the lower bound for the installation cost of the cycle.</p>
<div class="marks">[6]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Jonas’s network satisfies the requirement of there being less than a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> probability of the network failing after a power surge.</p>
<div class="marks">[5]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br>