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</div><h2>HL Paper 2</h2><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The company <em>Fresh Water</em> produces one-litre bottles of mineral water. The company wants to determine the amount of magnesium, in milligrams, in these bottles.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A random sample of ten bottles is analysed and the results are as follows:</span></p>
<p style="font: normal normal normal 28px/normal Helvetica; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">6.7, 7.2, 6.7, 6.8, 6.9, 7.0, 6.8, 6.6, 7.1, 7.3.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find unbiased estimates of the mean and variance of the amount of magnesium in the one-litre bottles.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\bar m = \frac{{6.7 + 7.2 + \ldots + 7.3}}{{10}} = 6.91\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s_{n - 1}^2 = \frac{1}{9}\left( {{{(6.7 - 6.91)}^2} + \ldots + {{(7.3 - 6.91)}^2}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{0.489}}{9} = 0.0543{\text{ (3 sf)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A0</em></strong> for 0.233.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates used a GDC to answer this question and many scored full marks in this question. However there were a significant number of candidates who showed little understanding of the meaning of unbiased estimate. In some cases, candidates wasted time by attempting to calculate the required values by hand.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The heights of all the new boys starting at a school were measured and the following cumulative frequency graph was produced.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img style="display: block; margin-left: auto; margin-right: auto;" 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IjWP6LxEAUP1mFQlWhyQL7UPNZVHjzhcListHzP3scE4cllt0XCQxTIl0FVoskB+VLzWFeZ8+gPivQ07xKEJ8fdFgkPUaSUr9414mweSZ60Dx5ZeM6cu8DkhUCF2j9i8hCrjIcfuQbyBU/B8zyw48H1lS5bzCtF/4jJQ6wyHn7kGiw7cOWhbsicp2jHy3hJrwg8THZbJDxEgXwZVCWaHJAvNY91lRXP+Ni48cIy23lY7bZIeIgC+TKoSjQ5IF9qHusqE57p6VBZafnw0LAgPAx3WyQ8RIF8GVQlmhyQLzWPdTV3nmg0WlO9ubOzUxAetrstEh6iQL4MqhJNDsiXmse6miOP8Sm9IvDQNQQPUSBfBlWJJgfkS81jXc2RRz/JFo1GBeGhawgeokC+DKoSTQ7Il5rHupoLz73b3GWl5dPTIUF4ROsfiXiIIqV89a4RZ5PlOkTwCMjjHzhVVlp+5Gi37SRi9o9EPMQq4+FHroF8wVMwPEMjZ9dXur555922k4jZP3LxEKuMhx+5BssOXHmoGzLnKfjxSp5k2/lIiwg8yQjSPzLyEAXyZVCVaHJAvtQ81lWKhsk72QThSQY8kG/mQL5ceagbQr5EDfU72SYnJwXhMQY8kG/mQL5ceagbQr7ZN9Qf1Ju8k812HlPAA/lmDuTLlYe6IeSbZcNEIrG9obHtQJsgPOkBD+SbOZAvVx7qhpBvlg3bDrTVVG823slWSPOnyHmIYhLZv/7myqdzTHbMLZAvVx7qhpBvNg2Hh4bLSstNb4AvpPlT5DxEMYksPPLDnT8Zvnz15ldM9s4jkC9XHuqGkO+aDfWHlqW/DbOQ5k+R8xAlTb6HfOffCjzf/qO9h/7X2eAn8YVFJh/DMLjJAjwy8pw5d2F9pUt/J5sIPKL1TwHwEKss9Uv1y7n5RU3TNHVuduqtF59ra9135H+/8X44tsDGnAyCI1+uPNQNmfMU2Hg9sOPB7Q2NpoeW2cgjWv8UBg9RLES2EP/03ZGuXd9aV+F0bPzOnq4XlX+MzKlMPjWXQL5ceagbQr4WDQ8e6kxf6rWRR7T+KRgeophEdn088PaNxbnZK2/2e+/f6KhwOqq+1doVuPzR7I1P33/d/2Tr471v/bO9R8GQL1ce6oaQ72olfan3yNFuQXjWrILHFvmGR1rvbdy+5TZHhdOx6T6v//X3r80ZVn0Xrw7uWNd49PKsjSvBkC9XHuqGkG/GUiKRqKnerC/1isCTTRU8NsnXs8G5busPu4YvX72RdoR768boE3/iqLjt0deuM/lwqkC+XHmoG0K+GUttB9q2NzTqL4EXgSebKnhsku/eJ3/x0eerHNguzk2f/OHXG3/ypp0rD5AvVx7qhpBveil5Va8gPFlWwWOLfL/8XSRy7b03zwWvLWiapiU+HvUfe3Hs4/gtJh/GJJAvVx7qhpCvqWS8qlcEnuyr4LFFvgvX3/qb76yrcN7eFVw6uP3y+ltPN3z3b966LsrFZpAvVx7qhpCvsaQv9SZfRWw7D1EVPHbId/HXgw/UtfyP505dvrZg/Ob9//kbh976nMkH5hzcZAEe8Xke2PHgXXfeoy/1isAjWv8UJA+xylK+Wgh2t74YNq34Lv568P6vOb/pe1+MtQfIFzyC8+hX9Z48HRCER7T+KVQeYpWlfLX46Ujbc29/brTsVzfeff7+dRVOtz9k/w0WmoZlB8481A2Z80g6XqZn9drOQ1EFDzUPUUwiu3Xjctf93/O+8NpbweC7bysB/09bv7WuwunYsu818wGxXYF8ufJQN4R8R98cS39Wr708dLsFjy3y1TTty2vK0/ff7nQ6Kpa2dd/+0eA/xgVRL+TLmYe6IeQ7+uZYZ2en6Vm99vLQ7RY8dslX07TFhZtXg8rZkcDLZ5WJ/z/yxeLKA3fYRI0EXx3qaqmscFZ2KDF1+ZsTJ7xup6PC5el7JzK/KjHkC/kKOV5HjnaXlZZPT4cE4RGtf4qBhyjZvcliYar/qVcjTD5Qm49M9LVU1rR0vaiEYivfjk901zYeVGZUbT6iHK6r7QnGM68xQ75ceagbFrl8T54OrK90DRwfEIRHtP4pEh6imES2uBC5fPxQa51x2UHfPAEW8lXjwZ66yuaeiUiqWedC/iaXV1mW8azi3drgn8poX8iXKw91wyKX77Zt9du21YvDI1r/FAkPUUxXO3wy8sNNTodzY+33WzzNK1vTvRuZyDc+0V27ZXfgE7NV1al+9waDbdWY0uFa5foKyJcrD3XDYpbvwPGB9ZWuoZGzgvDk0hA8ufAQJe0639ur3L2TCfOlvp++3Pt6zg/TmQv5m5y13n59tddR09I1GoqrmqapIX+DY0u7Mrv8k2pM6XA5mvpDGd4nB/ly5aFuWLTynZycLCstf6anTxCeHBuCJxceophEFnvP17Q9w9/7LE64qVP97g113sFgZF7T1PjUiZbKqrquiXgG1a4hX1M8rbuxYbNl2/lIyx/+wR9VV99hOwk22zdSI5qPIhfj7x8/0KWYnuTA5IRbTGmvNB7ezoX8TU5HU3/oC1L5WnxIARxJ2ctD3bA4j3z1J0YmEglBeHJvCJ5ceIiSKjJ1qt9dZT7VxuiEW9rawsp3sOwgDg91wyKU7+j50eS1ZSLwMGkInlx4iGIS2Rch/87bbr/3B8azbZ7m5sYtt+V+wi2mtFdWGa9hUEP+Bt2w6lS/e6v5oBgn3CBfkXhMVdNtxLbzsGoInlx4iJK27HBt9O/Opt1JzOaE26zi3eLaFZhZvqnCcEkDLjUThYe6YVHJN5FItLa0Gm8jxvwBD2ky3F58/b1Xnm8/0D12XdNu3Xh38OjzZz+88RWTD1NnArsra1r8H8Q1TY1c6vHs7A7eXKrhJgsxeKgbFpV8B44P1FRvjkajgvAwbAieXHiIkv5gnb/9zroKp2NDS0B/zfWt+Ad/v9P9U+Xalyw+To2HRrs9NU5HhbPWeyKYcquFGrnU46lxOqqWr4hYhRjyhXxtHS/92rLJyUlBeNg2BE8uPEQx3WRx9aWHv/3wkZ+/7v/xXyzJV9MWf/PSQxuEepi6RVXGX2aheKgbFol8z5y7YHxFhe08os2fIuchStpNFve/cOWrxYWgb++KfH89eP/XDC8WsjmQL1ce6oZFIl9P8y792jJBeESbP0XOQ5S0I98n+lPle+vzy09vdYj1MHW9a8TZPJI8aR88OfLozy3zD5wShEe0/ilyHmKVpX65cH30yD7fP/wq8JNm/7sfX3l71H+gTryHqdve+5JODvDkwqM/t+zgoU5BeETrH/AQq8z8jcXPrrz447p1FXiYevZVif4sWnO31A2Z84g2Xq0trdu21Ys2XuARiocoGUWmzs3+OqicHQkEXh69dCXyhTDi1TTIlzMPdcPClu/w0HBN9Wb9nZgi8KxZBY8tPETJ5mHqiwtzX4pxsk3TIF/OPNQNC1i+09OhstLy0fOjAo4XeITiIUo28v3iyguHB68yuc6XQSBfrjzUDQtVvsZ3Ygo4XuARiocoJpFdO/vopkwP1vnjrV3vmi+usSmQL1ce6oaFKl+frzf5TkwBxws8QvEQxSSy8Ijn7romj+GpOp4f1G7aWPv9lrbAx8JcamZRFf+XOcsq5CvCeJluZhNwvMAjFA9R0o58e89dSz2/thj/1fN7n2Z0ezGDQL5ceagbFp58E4lETfVmn6+XN20hzZ8i5yFKNmu+X3486PlG+5s3xLjoAfLlykPdsPDk29nZabqZTcDxAo9QPERZW76LczO/POIW6vZivWvE2WS5CBw82fNwupmtYPoHPOkbscpSv1zthJtTqCNf23tf0skBnix5hkbOrq90HXjiSUF4ROsf8GT8PrHKUr9MP+HW3PJoe/fgxY/jt1jZM8dg2YErD3VD5jw2jlfbgbbWlta80RbS/ClyHqKsfcItLSzeZJxDIF+uPNQNC0a++oJDOBzOWBVtvMAjFA9RsjnhlhombzLOIZAvVx7qhoUh35OnA8Y3s+WHtpDmT5HzECXrtxczfZNxLoF8ufJQNywM+W7bVr9tWz3FbjF/wEMak8g+D3Z915n69uLmxrs31X5/ZQm46d6NkG9qJJockK8Fz/DQ8PpK19DI2TzTFtL8KXIeoqSK7NaHxxoPjV5PfX/aQmjwhwdeurp8tSObNxnTB/LlykPdUHb56q+CP3K0W67xAo9QPERJe43Qo+lHtfFg171/8sPAWifi8hTIlysPdUOp5Zt8eo504wUeoXiIYhLZb0fbOkZmUu4kXvz8/zv6X/4YN1lYbLJchwie1XgOPPGkvuAgCI9o/QOebHiIVZb65eLc9Mld393dNXhu7N1gMHhZCfzP9sZNTsfX3L5fifNUM9t7X9LJAZ6MPP6BU8kFBxF4bN/AQ8dDrLK079yKf3jyR3cbr3n42nfaAyHcZFEQfxatuVvqhsx58jNe+oJD8lXw0o0XeITiIUpmkS3OXf+n4C/PBgIjr/0y+E/X58RY7dUD+XLloW4oqXwHjg8kH9eby24xf8BDmnSRfXn9vVeebz/QPXZd027deHfw6PNnP7zxFZMPYxLIlysPdUMZ5au/Hyj5uN5cdov5Ax7SmER268blv/3OugqnY0NLQL+98lb8g7/f6f4pnudbGJMD8k3ymBYcctwt5g94SJMqssWrLz387YeP/Px1/4//IrB8b/vib156aMM3Dr31OZMPzDmQL1ce6obSydf4fqDcd4v5Ax7SpF3ne/8LV75aXAj69q7I99eD939NqEvNLKqQb4481A3lkq/p/UC57xbzBzykSTvyfaI/Vb63Pr/89FZHhdPtD+EdbqtEoskB+WqatvORlprqzaYFhxx3i/kDHtKYRLZwffTIPt8//Crwk2b/ux9feXvUf6BuXYXTsWXfa2FBLnnAdb7gyXGrrr5jfaXrzLkLtpOI2T/goeMhVpn5G4ufXXnxx3XrDM8wW/ftHw3+Y1wQ9UK+4Mlt6zvWX1Za3nes33YSMfsHPNQ8xCpL/XJx4eZv3r/yzzdnfx1Uzo4EAi+PXroS+UIY8Woalh0481A3ZM7DY7z0FxJXV9/Bdrc50hbS/ClyHqKYnud79aWdG52Opv7QHJO98wjky5WHuqEU8u3s7Kyp3rzzkRa2u82RtpDmT5HzEMUk338afOA//0nrLz5dMB3s/utvrnzKyMezinfL8ppGVYN/KnkaT41MnPC6nY4Kl6fvncj8au0hX6481A3Fl2/yCodCGi/wCMVDlLRlh2tvHt379JnpGwvGb954628OvMLkAerqTGB3ZXJB2XCIHZ/orm08qMyo2nxEOVxX2xOMZ766AvLlykPdUHD56gsO+hUOhTRe4BGKhyglmqZpC/Hf3Zxb1CxfI8Tm7RU3g13N7cps2vfnQv4ml1eJLX05q3i3Gg+KU4ghX8iXvKovOOi3VBTSeIFHKB6ilGiLs5f/pvG2rx8e+1zVtC9C/p23pb5GiOWrg2JKe2WFs9bbH7gYMh7YqlP97g0G26oxpcO1ypXFkC9XHuqGIsvX9AyHQhov8AjFQ5QS9ergn6274+Fnxq8vapqmJqZf/OkvPjJf3sDm1UFzIX/TyqF0bcdIaOlIVw35GxxbDEfEakzpcK1y3g/y5cpD3VBY+aY/w6GQxgs8QvEQpWQh2LPj2AfLTy0Ljzzqy3Qb8fXxwNs3mHygNh8JvtbvdTsdFc6lhd101UK+kC+z8TI9NJKahx8teAqGhygl2udjzxwd/TSuGzejfBcXPn+390k2J9yWMx9RDtctHe0Sy9cUT+tubNgybt974PtlpeXb//v9tpNgK/iNVIIlmvbltTd/+p11mU6ysT/hZsys4t2in2TDsoM4PNQNBTzyTb4WkwkPP1rwFAwPUXSRfXn9vXPHu9r3er5f96d33/dI6tk2j+cHtRs5yHcu5N+5dJJNnep3bzXIdy7kb1rtUT6QL1ce6oYCynd4aLimenM0GmXCw48WPAXDQxSTyFZZ8/3qg2OMlx00TZtVOn6mxHS/4lIzUXioG9Fmwv8AACAASURBVIom35OnA2Wl5aPnR1nx8KMFT8HwEMUksn/9eOLD2QyPcmBxh5saCb5yLqjfuqZG3nm24yllZkWvuMlCDB7qhqLJd9u2+vQFh1x4+NGCp2B4iGIlMsZRZ5QOt9NR4XTUtHS9qCxfZ7ZSj1zq8dQ4HVV13sEgbi+GfHP4xIOHOstKy9MXHHLh4UcLnoLhIUoe5csokC9XHuqG4sg3Go2ur3QdPJThWem58HCiBU8h8RAF8mVQlWhyFIN82w60bdtWXyTjBR6heIgC+TKoSjQ5Cl6+42PjZaXl/oFTRTJe4BGKhyhSylfvGnE2jyRP2i94njPnLqyvdB144klBeETrH/Bw5SFWWdp3vrz+3ivPtx/oHruuabduvDt49PmzH974KkNTmwL5gme1bc/ex7J5OVvR9g94uPIQqyz1y1s3Lv/td9ZVOB0bWpbfXhz/4O93un+qXPuSiTpzD5YduPJQN2TOQ/qJxkeXFc94gUcoHqKkvTr+4W8/fOTnr/t//BdL8tW0xd+89NCGbxx663MmH5hzIF+uPNQNbZev8U7i4hkv8AjFQ5RUkS0Eu+9/4cpXiwtB394V+f568P6vOW/vyvS0MxsC+XLloW5or3xNdxIXz3iBRygeoqQd+T7RnyrfW59ffnqro2K1Jy3kP5AvVx7qhjbKNxqNlpWWDw8Nc+VhRQueAuYhiklkC9dHj+zz/cOvAj9p9r/78ZW3R/0H6tZVOB1b9r0WFuQF8pAvVx7qhjbKt+1AW2tLK28eVrTgKWAeoqSJbPGzKy/+uM74hMl13/7R4D/GBVEv5MuZh7qhXfLV30k8PR3izcOEFjyFzUOUjCJT52Z/HVTOjgQCL49euhL5Qhjxahrky5mHuqEt8tXfSezz9eaBJ3da8BQ8D1FMIrt2tnvo6oJQsjUH8uXKQ93QFvmmvyKIH0/utOApeB6ipD3P17NxY+OB5wOXr94U6MYKY3CTBXj0TX9i75Gj3YLwiNY/4MkzD7HKUr+8Ph54+8bctfdfP3Hk0eZ9XaffunJ9TrDjYMgXPPr2wI4HH9jxoDg8ovUPePLMQ6yy1UtffXb18kjvj1s8h144+6trc2JcaIZlB8481A2Z81jv85mevrLS8nA4nLFaPOMFHqF4iGISmfrl3PzSke7CjauXh5/Z497oqHA6nBt3nv5YDP1Cvlx5qBvmU76JREJ/gE4+eahpwVM8PERJW/N9yh/89MO3Tj/9w7urnI4Kp2PTfft7Ry5/9JkwZ+EgX6481A3zKd+B4wP6A3TyyUNNC57i4SFK+gm3DUuX997+vQO9rwQ/jYlxU/FKIF+uPNQN8ybfcDhcVlr+TE8fxgs8ovEQJePVDt4XzgY/jYtm3aVAvlx5qBvmTb76/WwYL/AIyEOUNPk+2X/lK1FWGDIG8uXKQ90wP/JN3s+G8QKPgDxEWf2EW0qujwfevsHkA3MO5MuVh7phHuSbSCS2NzTq97NhvMAjIA9RSrS56ZGnnvhJYHpO0zT1U6Wvu7ury7z9dE9dayDC5ANzDq7zLVqeg4c6s3lRRdH2D3js5SFW2a0rx/6bo8L5X49duaVpWnTs0LdXHqlj3DyQr/STQ2qeoZGz+gvhBeERrX/AYzsPscq0xc8/HrswfvXzRU3TtMX59/7O03Xx00hqPr3Y3f6KOPK1qFr0gnUH5VKV6M+iNXdL3ZA5j6nU2dm5vaHRRh4iWvAUJw9R0h8pGf+Xf0l9fuRCbPaz+O8iNwS5+gHy5cpD3ZCrfPX3sxmfG4nxAo+APERJe6rZj//X+7dSv7fwydkn249/+Jkg10BAvlx5qBtylW9rS2vy/Wx28WRPC56i5SFK2qVmj/rM72pbjF954aHbHhi8ituLV4lEk0NG+Y6PjZeVliffz2YXT5a04ClmHqLoIlv86uqZjsZNmU+1OSqcjgrItzAmh3TypXtcevGMF3iE4iGKQWQLvw2+sHvTui33PdLc4jFurXvb+85Ox7DssFpVoskhnXz11xKTPi69eMYLPELxEMX06viPXtrzvHnZYeF3H/9GlLNtGuTLmYe6IQ/5Do2cranebHwtsY08a9KCBzxEMYlscWHuS7NnF6NvH/3R4bf+BUe+q1UlmhxyyXfP3seMl5fZy7MmLXjAQ5Q0+V5Tuh+6+7b0Zd+luzDsD26yKBIe/8Cp5NPLROARrX/AIxoPscpSv/zt6ON3OG+/9wee79f96d1Li79N92666+GnfvGhIG+Ph3yLhIf6LUFF0j/gEY2HWGUpXy0Eu7/79Nuf39K0m28f/cnIta80TdMWPnpp7xMvXTWf8bArWHbgykPdkC2PfleFf+CUIDxrVsEDHtKkiuzWe72P/iK8qGna4vx7x/7i2PtzmqZpC5HAnj/5YeCaMEe+FlXIN0ce6oZsebY3NHqad4nDs2YVPOAhjUlk0bFD9//Ae/SZF/4hFPvN2X1//uTpX7771qkn677mvL3LfBWETYF8ufJQN2TIo99VMTRyVhCebKrgAQ9p0k+4vXn0e5uc6x7qn04sfBr40Z86nY4Kp+Nrbt+vmK47zM8E9rnc/pDhxg01MnHC63Y6Klyevnci86sSQ74FLd/kQ3sxXuCRjocomUS2EP/dzTn9IWcL199//eVXRt/+hO3ZNnUmsLuywmmUb3yiu7bxoDKjavMR5XBdbU8wnvmOOsiXKw91Q1Y8ybsqMF7gkY6HKFYiM4TpmyziE92ex9s9NQb5zoX8TS6vElv6iVnFu7XBP5XRvpAvVx7qhkx49JuJ9bsqMF7gkY6HKCVqWPm79FdXcHyTxc1g1+PdwZDi3bIiX3Wq373BYFs1pnSYFiVWiCHfwpWv8WZijBd4pOMhSon2+VtPfd1p8Ugdpm+yUONBX0vXRFybNcpXDfkbHFvaldnkj8WUDpejqT80l4EY8i1Q+Uaj0ZrqzaPnR3P/xOIZL/AIxUOUEk2Lv+/b3z12NWIRVm+yiE90e3zBuKqlyDddtWvI1xRP625sBbB98867/9O622zHwIaNbiPVYYmmaYv/+tlnC9Yn1L5k8SaLm8FnfzYyo1/GkJN8LT4DR7458lA3zJEnGo2WlZaPj40z+cTiGS/wCMVDlGxOuGV62g5x1Hjw2MHAJ8uruFh2WKNabPL1+XpNz9DBeIFHOh6iZCPfL668cHjw6pe5fdCs4t2SaTW5qsE/papT/e6tBvnOhfxNTpxwKxr5ph/25viJxTNe4BGKhyhp73B7NOP7LP54a9e7TG+ySDnyxaVm4vBQN8yFx/Rm4tw/sXjGCzxC8RAl7R1unrvrmjyG11h4flC7aWPt91vaAh+zfI2QSb64yUIUHuqG1Dz6oyONbybO/ROLZ7zAIxQPUdKOfHvPmR6gsxj/1fN7n1au5bjsYEqafDVNjVzq8dQ4HVV13sEgbi8uGvk+sONB05uJc//E4hkv8AjFQ5Rs1ny//HjQ8432N2/gqWarRKLJIZp8VzvszfETi2e8wCMUD1HWlu/i3Mwvj7jxVLPCmByiyVd/YjrzTyye8QKPUDxEyfKEm1OoI1+9a8TZPJI8aV80Hv2w1z9wShAe0foHPHLxEKss9cv0E27NLY+2dw9e/DguxhvcIN8C4uH3oqDC6B/wyMVDrLLULzOccBMtWHbgykPdkJQn+aIgjBd4CoaHKHY8UjK3QL5ceagbkvK0HWhrO9CG8QJPIfEQJU1kCzdCb/3iWDe/R0rmGsiXKw91QyKecDisX+SA8QJPIfEQxSSy2Hu+HbdxfKQkg0C+XHmoGxLx+Hy9rS2t1g0xXuCRjocoaa+Ov935jcdP/Z+rM1weKckikC9XHuqG2fMYn+SA8QJPIfEQJVVkizNn9/yXh1/8TdopNyaPlGQTyJcrD3XD7HmMDzDDeIGnkHiIkv724jcO7/V/OGe6xfjTl3tfv87kA3MO5MuVh7phljymB5hhvMBTSDxEMYtsMT410v69bzXuTLnUt+nejSKt+epdI84my3WIIvDs2fvYXXfeIw6PCBt4CoOHWGUpXy1eG91/N893uDEI5Csvz5lzF9ZXup7p6ROER5ANPIXBQ6yylK8Wgt23//HWp16/Npf6OMeFqf6nXhVHvhZVi16w7qBcqhL9WbTmbqkbZsNjfDnxmg0xXuCRjoco5kvNgl337xj8ddoJt4XYzbggN75Bvlx5qBuuyZNIJGqqNw8PDWfZEOMFHul4iJK+5vv+8ba+tz9PfZIDjnwLZXLYKN/R86Omw17rhhgv8EjHQ5RUkalT/e4q8dd8Lar4Zc6Rh7rhmjzbGxoHjg9k3xDjBR7peIhiEtkXIf/O226/9wfGSx3Eu9rBoopf5hx5qBta84yPjZeVlkej0ewbYrzAIx0PUdKWHa6N/t3ZsOkq34W50C9wnW9BTA675Lu9odHn6yVqiPECj3Q8RMnbq+OZBfLlykPd0KL6vQe+n/Gw17ohxgs80vEQxa5Xx9MH8uXKQ93Qorrh9q9nfEWmdUOMF3ik4yGKXa+Opw9uspCL5+TpgC3vCpKlf8BTMDzEKkv9Mm+vjqcP5CsXz569j62vctmOIWz/gKdgeIhVlsXP4NXxhfNn0Zq7pW6Ysao/Rue79Y0Uu8V4gUc6HqLg1fEMqhJNjjzLd3hoeHtDIx0Pxgs80vEQRcpXx1tU8cucIw91w/Rq8n5iyBc8RcJDFClfHW9RxS9zjjzUDdOr42Pj+v3EkC94ioSHKHh1PIOqRJMjn/JN3lgB+YKnSHiIYhTZ4kI8OhtfSPnOv3z0Tze+YvJJrAL5cuWhbmiqTk+HkjdWQL7gKRIeopRoWux9/+P33VXldFR9y/PTU8HrxgPfxfjUy0d/durDz8Q5GoZ8ufJQNzRV2w60JW+sgHzBUyQ8RCnRNG3x6uCOP939wuV/nsuo2K9Cg7t/MnpdjGsdcJ2vDDxDI2fLSsv7jvULwiNa/4CnIHmIVaZp85++6O1Qfrv6se3iF2Od3/H9n/mcnMkskK/4PAeeeNL4ojbbeUTrH/AUJA+xyjTtt6NPdI19YbmuEAm0uP0hYW4vtqha9IJ1B+VSlejPojV3S90wWdWvMBs9P5ojD8YLPNLxEKVE08Ijj/qsb6BYDL/4MG6yKIjJkQf56o/uNb6xAvIFT5HwEKVE026MHXrc8omRt6KjP3b912NXGFzpOx+Z6GuprHA6quq8gVA85VhajUyc8LqdjgqXp++dyKqLHJAvVx7qhslqa0ur6dG9kC94ioSHKCWadis62v7f2s9fW8i88rAY/9Xz39twx5HLX+T6WWp88pUTExFV09TIpR5PjcurxJLF+ER3beNBZUbV5iPK4branmA88zIH5MuVh7qhXg2Hw2Wl5eFwOHcejBd4pOMhSommadrc+8e+t+lbj/rOBq/eML40fiH26buBow/d4Vy3s386d/devXgxvLx3NaZ0uCo7lJj+jbmQv8ng4lnFu7XBP5XRvpAvVx7qhnrV5+ttbWllwoPxAo90PETRRba4cO2Nn9R9zemocDo2Lt1e/Ejj3ev0Bzvc+cPBK3NMPm0lcyH/zrquibj+lTrV795gsK0aUzpcq5zig3y58lA3HH1zTD/VNj42zoQH4wUe6XiIkhTZ4sL1d0+1378x9Xk6Gxvbj1++xvhMWzyk+DtaOt6IJF0b8jc4trQrs8s/ocaUDpejqT+UwfmQL1ce6oajb44lH+bAhAfjBR7peIhiEpk6N/vRe2OjLwcCI68pb1/55/gqC8G00a1a4XRUOGs7RkIxwzeNqoV8pZRv+qm2XHgwXuCRjoco2TxMnXnmI8HB9toqZ+W+kZl5Cvma4mndjc327c+aHiorLf+zpodsJ8GGzZaN1IO2yFfTUpcasOwgDg91wwNPPLm9IfMbK+h4MF7gkY6HKLbJV1On+t1bl4Rr/G9N0y9+cOKEm1TyXV/pMt7VljsPxgs80vEQxT75xpT22/VlBw2XmonDQ9ew71h/8gGSrHgwXuCRjoco+ZOvOhPYXeluH9DvsphROppa/B/Ek2XcZCEGD+UnNu/yNO9iy4PxAo90PETJ45Fv/IN+T41+EZvL0zUSjJjkqt/25nRU1XkHg7i9WB75JhKJstLyZ3r62PJgvMAjHQ9R7Ft2oA3ky5WHouH42Pj6SteZcxfY8mC8wCMdD1EgXwZViSYHD/m2trTu2fsYcx6MF3ik4yEK5MugKtHkYC7faDSafGkFWx6MF3ik4yGKlPLVu0aczSPJk/Z5bEeOdq+vdInDI1r/gKd4eIhVxsOPXAP5CsWzbVu9vuYgCI9o/QOe4uEhVhkPP3INlh248hA11NccwuEwDx6MF3ik4yEK5MugKtHkYCvf4aFh/ZZiyBc84CEN5MugKtHkYCvf7Q2NA8cHOPFgvMAjHQ9RIF8GVYkmB0P5Gt8YBPmCBzykgXwZVCWaHAzlO3B8IPkYM8gXPOAhDeTLoCrR5GAo3+SaAycejBd4pOMhCuTLoCrR5GAlX9NbiiFf8ICHNJAvg6pEk4OVfI1rDpx4MF7gkY6HKFLKV+8acTZZLgJnuN115z0HnnhSHB7R+gc8RchDrDIefuQayNd2npOnA2Wl5SdPBwThEa1/wFOcPMQq4+FHrsGyA1eebBqa1hw48WC8wCMdD1EgXwZViSYHE/lub2gcHhrmzYPxAo90PESBfBlUJZocuctXv87B9Lo2yBc84CEN5MugKtHkyF2+A8cHWlta88CD8QKPdDxEgXwZVCWaHLnLd3tDY/or4iFf8ICHNJAvg6pEkyNH+U5OTmZ8RTzkCx7wkAbyZVCVaHLkKF+frzd9zYETD8YLPNLxEEVK+epdI84my3WIuW/rK11HjnaLwyNa/4CnmHmIVcbDj1wD+drF03esv6y0fGjkrCA8ovUPeIqch1hlPPzINVh24MpjUdqz97GMaw6ceDBe4JGOhyiQL4OqRJMjF/mur3SNj43njQfjBR7peIgC+TKoSjQ5qOX7TE9fWWl5IpHIGw/GCzzS8RAF8mVQlWhyUMvX07zL07wrnzwYL/BIx0MUyJdBVaLJQSffRCJRVlr+TE9fPnkwXuCRjocokC+DqkSTg06+42Pj6ytdZ85dyCcPxgs80vEQBfJlUJVoctDJt+1A2569j+WZB+MFHul4iAL5MqhKNDko5BuNRstKy/uO9UO+Ao4XeITiIYqU8tW7RpxNlovA6bYjR7vXV7rE4RGtf8ADHn0jVhkPP3IN5Jtnnm3b6vU1B0F4ROsf8IBH34hVxsOPXINlB648pu8kXxGffx6MF3ik4yFKfuUbD13oanY5KpyOqjrvYDAybyyqkYkTXrfTUeHy9L2TWjIG8uXKY/pO8nVtkK91FTzgIU0e5at+8uqzxy6EYpqmqZFLPZ4aZ21PMK4uVeMT3bWNB5UZVZuPKIfrjKXUQL5ceUzf2d7QOHB8wBYejBd4pOMhSv7kq3506eLMyvGsGvI3OLa0K7OapmnaXMjf5PIqsaXirOLd2uCfymhfyJcrj/FL4+vaIF/rKnjAQxr71nxjSnvlsnzVqX73BoNt1ZjS4XL7Q5nsC/ly5TF+aXxdG+RrXQUPeEhjq3xv3zcyM6+Zj4K1Jfk6mvpDc+ntIF+uPMYvja9rg3ytq+ABD2nskq8aU55q6JqIL/23SbWQr/3yNb0iHvK1roIHPKSxSb7xiW6Pb/mUGrF8TfG07sbGfLvnW1v/07rbbMfAhk2WjdSCtsj3ZvDZw/1TseTXWHYQhyf538nrHOziwXiBRzoeouRfvvMzrxw7YTCvpukn3LYa5DsX8jc5ccLNPvnqz3MIh8M28mC8wCMdD1HyLN/5iHKsR5lZlmpsamDwYkzFpWbi8Cz9x/lR/d4KG3kwXuCRjoco+ZRvLBToqHNUOI1b8vAWN1mIwaP/R9uBNp+v114ejBd4pOMhSt7kOz8T2OcymddRZTy8XbrtLdOdx8ZAvlx5tOX3VkxOTtrLg/ECj3Q8RMGDdRhUJZoc2ch3fGy8rLTcdh6MF3ik4yEK5MugKtHkyEa+Pl9vZ2en7TwYL/BIx0MUyJdBVaLJkY18a6o3J29ss5EH4wUe6XiIIqV89a4RZ/NI8rDnbDb/wKmy0vKhkbOC8IjWP+ABz2o8xCrj4UeugXy58hx44slt2+rF4RGtf8ADnqKWr0XVohesOyiXqkR/Fq2529aWVuONbTbyYLzAIx0PUSBfBlWJJod1w6GRs6Yb22zkwXiBRzoeokC+DKoSTQ7rhkeOdtdUbxaEB+MFHul4iAL5MqhKNDnWaNi8y3Rjm408GC/wSMdDFMiXQVWiyWHRUL+xbXxsXBAejBd4pOMhCuTLoCrR5LBoODk5WVZankgkBOHBeIFHOh6iQL4MqhJNDouGPl/vAzsepPtEyBc84CEN5MugKtHksGi4vaHxyNFuuk+EfMEDHtJIKV+9a8TZZLkI3GI7eTrA/Ma2Quof8IBnTR5ilfHwI9dAvjx4Dh7qvOvOe8ThEa1/wAOeNXmIVcbDj1yDZQcePPqNbUL1D8YLPNLxEAXyZVCVaHJkbKi/sW1yclKo/sF4gUc6HqJAvgyqEk2OjA1Hz4/qN7YJ1T8YL/BIx0MUyJdBVaLJkbFhZ2enfmObUP2D8QKPdDxEgXwZVCWaHOkNjTe2CdU/GC/wSMdDFMiXQVWiyZHeUH9jm35jm1D9g/ECj3Q8RIF8GVQlmhzpDY1vbBOqfzBe4JGOhyhSylfvGnE2Wa5DzLitr3Q909MnDo9o/QMe2zdZeIhVxsOPXAP5MuTpO9bP78a2Augf8IiwycJDrDIefuQaLDsw5PH5eltbWo1Vuk/k0T8YL/BIx0MUyJdBVaLJYWpoeku8UP2D8QKPdDxEgXwZVCWaHMaG+gN8o9GosUr3iZAveMBDGsiXQVWiyWFsOHB8wLjmoEG+Yo8XeMTnIQrky6Aq0eQwNtze0Ghcc9AgX7HHCzzi8xAF8mVQlWhyJBtOT4dMaw4a5CvweIFHCh6iQL4MqhJNjmRD03UOySrdJ0K+4AEPaSBfBlWJJkeyoek6h2SV7hMhX/CAhzRSylfvGnE2WS4CT275ubdC3v4Bj+0MMvIQq4yHH7kG8s2dZ8/ex7ZtqxeHR7T+AY/tDDLyEKuMhx+5BssOufPUVG/WnyGZXqX7RB79g/ECj3Q8RIF8GVQlmhyjb44909OXfIZkepXuEyFf8ICHNJAvg6pEk2P0zTFP867kMyTTq3SfCPmCBzykybt84yEl8PNuj7tdmTVV1MjECa/b6ahwefreicyvtgPINxeeM+cuJN9bkXG3dJ8I+YIHPKTJr3zVqf7GppadNU7HFrN84xPdtY0HlRlVm48oh+tqe4JxNeM+IN9ceI4c7V5f6bLYLd0nQr7gAQ9pbFh2UEP+BrN850L+JpdXiS19Oat4tzb4pzLaF/LNheeuO+/Zs/cxi93SfSLkCx7wkEYM+apT/e4NBtuqMaXD5faHMtkX8qXmCYfDZaXlJ08HLHZL94mQL3jAQxoh5Jv2HTWmdLgcTf2hufTmkC81j8/Xq1/ea7Fbuk+EfMEDHtKIIN901a4hX1M8rbuxrbntfKTlD//gj75b32g7CTZsBbmRmlBK+VrsHEdSq/GMj43XVG8+c+4CjnylGC/wyMhDFBHki2WHfPC0trT6fL1r7pbuEyFf8ICHNELIV1On+t1bDd+ZC/mbnDjhxo5Hf3pvOByGfKl5rKvgAQ9pxJAvLjXjzOPz9bYdaMtmt3SfCPmCBzykEUS+uMmCI080Gk3e1Qb5UvNYV8EDHtLkWb6zineL01GxtKUuLKiRSz2eGqejqs47GMTtxex4Bo4PbG9ozHK3dJ8I+YIHPKTBg3UYVEWeHIlEwvjSCsiXmse6Ch7wkEZK+epdI87mEfhhzwcPda6vdOlXmInAI8IGHvDw4CFWGQ8/cg3kmz3PmXMX1le6Dh7qFIRHkA084OHBQ6wyHn7kGiw7ZM+j31hhfG76mrul+0Qe/VOE4wUe2XmIAvkyqAo7ObY3NA4PDRPtlu4TIV/wgIc0kC+DqpiTY3ho2HTYm81u6T4R8gUPeEgD+TKoCjg59IscTIe92eyW7hMhX/CAhzSQL4OqgJMj42FvNrul+0TIFzzgIQ3ky6Aq2uR48OFHMh72ZrNbuk+EfMEDHtJAvgyqok2O6uo7kre0ke6W7hMhX/CAhzRSylfvGnE2oa5D9A+cKist7zvWbzuJmP0DHvBw4iFWGQ8/cg3ka7GdOXfhrjvvqa6+w3YSMfsHPODhx0OsMh5+5BosO1hUB44P1FRvfvDhR6h5qBsy759iGC/wFBgPUSBfBlVBJof+xPTR86O58FA3hHzBAx6iQL4MqiJMjkQisb2hUX9iOuQr/niBpyB5iAL5MqiKMDk6OzuTF/ZCvuKPF3gKkocokC+Dqu2TY3houKy0fHo6lDsPdUPIFzzgIQrky6Bq7+QYHxtPviUodx7qhpAveMBDFMiXQdXGyREOh8tKy32+XlY81A0hX/CAhyhSylfvGnE2u65DPHk6sL7StWfvY4LwiNY/4AFPPnmIVcbDj1wD+eqbbt5t2+rTXxEky2QFD3gKiYdYZTz8yDVYdtA0TTdva0tr+nPLcuShbsi8fwppvMBTJDxEgXwZVPM8OaanQ/oxb0bz5shD3RDyBQ94iAL5Mqjmc3Lo1zbo67w8eKgbQr7gAQ9RIF8G1bxNjoHjA2Wl5QPHB/jxUDeEfMEDHqJAvgyqeZgciUSi7UBbTfVm/XpeyFfw8QJPcfIQBfJlUOU9OSYnJ2uqN29vaAyHw7x5qBtCvuABD1EgXwZVfpMjkUjoSw2dnZ3G02uQr5jjBZ4i5yEK5Mugymly9B3r397QWFO9eXJyMm881A0hX/CAhyhSylfvGnE25heBD42cfWDHg2Wl5Z7mXen3UOSfR7T+AQ94BOQhVhkPP3JNYcv3zLkLB554sqy0/K477/EPnLKdR7T+3c1xTgAAC69JREFUAQ94bN+KWr4WVYtesO6gXKpM/ixKJBLDQ8M11Zv1Sxrs4qFuyJxH8PECD3hyDOTLoJrj5IhGo0ntDg8N6yfWIF9hxws84FmtRBTIl0GVenL4B07t2ftYWWn59obGpHZt5BGqfwQcL8gFPNY8RCk6+U5OTjY3N6c/FSF5ENrc3ByNRrPfrUY+OaLR6Oj50e0NjWWl5Q/seND4HPQsP1Eu+VoMGeQLnkLiMSYajW7atGloaGi1Z7AUnXzr6+tLSkqee+65jNXnnnvOokqBZGwYjUbHx8bbDrSVlZbXVG8eOD5w8nSAx+Sgk51WNPLNpX9EGy/wCMVjTCKRGBoa2rRpU319/dhYhr0Vl3y7e/pKSkqGhoZKSkqSd4slq0MjZ0tKSvbv319SUmI6+M1lcvgHTg0PDbe2tOrO9fl6k9ftCjhZqRtCvuABT3qi0ah+SLd///7p6emU/WS/F95RIxMnvG6no8Ll6XsnMr/aj+Ui3zu+eZd+VLt///79+/ebqn+596/q6+s1Tauvrzcd/BINRiKRmJ4ODQ8Ntx1oW1/p0pd0B44PEN0rAflCvuCRjme1hMNh/ajuueeeSx7YCSPf+ER3beNBZUbV5iPK4branmBczfiD1PLVD3v1/+fT09MlJSVGG+qHvfpfB2NjY6aD3zUHY3JycnhouLOzU1/J1YXr8/U+09M3NHKWghbyhXzBIx2PdSYnJ+vr65MLwYLIdy7kb3J5ldjSl7OKd2uDfyqjfUsIk3ToHd+86y/3/lVyP88995x+nKvnL/f+1R3fvIvuU/7t7/3bstLy//jv/uN/+Hf/77///X//+//m93/v//k9Uk4EQYonQ0NDYshXnep3bzDYVo0pHS63P5TJviUk/+wkFxDSD2aT5yL1/y4pKenu6cvh/wOCIIhVpqenjYsPQshXDfkbHFvaldnkN2JKh8vR1B+ay3HPSeemL+Nqmqafi9RXxI1HwQiCIAyT8bSbCPJNVy0z+WqaVl9fr19eln71biKRqK+v1/8tyngtCIIgSC4xXnBmOuVe+PLVD37TD3v1TE5OlpSU4LAXQRDmGRsb27RpU3J50xQR5Mtx2UHP0NCQ6apeY86fP2+6/g5BECTHhMNh/bBP7Dvc1Kl+91aDfOdC/ibnKifcEARBpEj6UqcxYsiX5FIz+6LGQxdHhrpabu9QYpZoaiQ44K1zVDgrm3smIrz+X8RDSuDn3R634R+tzDTZYucJSY2HRrs9NU5HhdPhbh/g10GxkPLKcFfzxpV5lTHzkYm+lsoKp6OqzhsIrXJ1OZtkO2QrbDOBfatd9pNzsuwfbfkv0QqnvnE8KsoeSdM0TY0EXx3qaqmscFbyn9scIoh8CW6ysCtqyH/fzuY/X3ukbwa7dtR1vBFRNTXyxsHaHd3Bmxxopvobm1p21jhTlmsy/WC22HlCUmfO9Tw7Goqry9arquuaiLOnmQv5d/25Z4fLUeGy+k1W45OvnJiIqJqmRi71eGosfzi3ZD1kKy1mArsrOckuy/7ROT4Z2VWzZF5HFbejIhKkpclT09L1ohLiNWK8I4x8l2e/01FV5x0Mrn57sa2ZC/mbrC2mhvwNKz9gdcFy7klbK18ta2PnC2nuo4uXZ1YoOIOpU/3uKqvfZPXqxYvhlKvLOfdS1kOmafGJbs/j7Z4ajkeaa/aPpmmaGg/2NPD7N4kWqY7rn5V5iUDylSFryiJttTqmtFcyO3NoioTyNf84X99l9ZuczFzIv5PPYbiBKNv+uRnserw7GFK8W+yW76zi3eJ0uNv9gXwcY2aDFJ/ort2yO/CJ1ObVIF/CrGWx9KkTU9oref2lVhjy3bgrMGOnXDRN07R4SPF3tHS8wftQKrv+UeNBX0vXRFwXn63yVUP+huRqr8PdHpji+o9TFkhzIX+Ts9bbr6/2Ompaukb5rtRzC+RLlLUslq5ayNcqs4q3mcua+BJNVn/DrpxNqu0Y4Xxwl1X/xCe6Pb5gXNUEkO/SD0aCr/q9dY4Kp6OR43hlg6RO9bs3LK9MqvGpE9xOG3AP5EsUyJcVkmY4vuNHk/2yw3wkONheW+Ws3Dcyw/F8Qxb9czP47M+WGUSR79KPR944WEvw81yQYkp75RbzZans7gnIZyBfomDZgRWSpsUneryDU1z/YCSVC9lhOxXRGh+hxoPHDq6sZool33yck1wLKb0D8zBqnAL5EiWrE27GqaOG/A3c/lmWWL7qJ68++yJf82rkcjHf7MOBaI3+0c9uVaRtfP79Jpavpob8DVzvfsrqyDelN7j+inEN5EsUXGrGAkmdUZ49piSvJox/cMJ/ictfsqRyiSntt9u+7GCMgEe+PzvI9RhzbaRZxbvFtXKSlu+vGNdAvkTJZDH1k5FdWwxL/nm5yUL/5Ay/yfMzgX0u8y0q9so3FSk+NeJ15+OwTsv8m6zOBHZXLp01UmcCuyuX77JTZ5SOphb/B/m/1MyIlBo75Jsyn+cjwXOvBvVrQOYjE8faD3G+IGRtJL27avSRUiOXejw7+Z4D5BbIN+vElPbKTL4wy1fT1Mg7zza7HBXOWu+JIKe5mvr36crvZ5p8V8O2BSnlXqnkxuNvxtQ7Yg0fkWK6+Af9Szc6V7g8XSO8BkvPav1ji3xX7R+zfJXDdcv9M6yEeP7LlCWSlnKHOsdfMe6BfBEEQWwI5IsgCGJDIF8EQRAbAvkiCILYEMgXQRDEhkC+CIIgNgTyRRAEsSGQL4IgiA2BfBEEQWwI5IsgCGJDIF8EQRAbAvkiCILYEMgXQRDEhkC+CIIgNgTyRRAEsSGQL4IgiA2BfBEEQWwI5IsgCGJDIF+kCJL+qqdVfi4eujjcteu+HF62pEYmTnT4CF6XF7vY3REI8X6RMyJeIF9E8Jjepq6/2sv0vq+13k2XpXyX3ndH/6Y7NfLGQc9TIyGidzHPRyb6WtyHV17njBRHIF9EhsSU9sp0J3J4v6Q61e/esKp81fDFi1dX/bT4RLf7cao3z6vxqRO7d52YwvFvMQXyRWSIEPJV40Hf7lUPiudC/p05vBw6x+aIfIF8ERkignzjE921qx8Ux5T2SsPbzik+OeRvqOwgWCxGJA/ki8iQbOUbC73R01JZ4XRUuDw9F5bWXvXTaM0bvcryWqwaD412e2qcjgpnbUfKEu2SfK/EQoH22iqno6bF/0Fc081btbzEvKVdmU3lU2NKhyuFZOVDP4tc6vHUOB1VdR1vRNT5SHAwZc8pH701bc9IwQbyRWTI0qmwTNuK8m4Gn32qZyKiapqmxab8u1z6geRyW1dSvjGlvdJ9UJlRNTU+dUKXtVP/YXWq372hbtfPTkxEVG1+JrDP5Vg+nrVakZhVvFtW9m8Adnm6RoIRVVPjwZ46R01L14tKKKZp8xHlcJ0j9UjZerkZKbhAvogMyebIN4Oglw9R1al+d9WyHNWY0uFa+QN/VvFuXbkQItWAasjfkLKTVeSYsv9Vvpn6fyFlz4b/O+adIIUbyBeRIWvLN/0Pf0PWkK/B4HbLl/ESNiJwIF9EhmQpX8cqp7xMHlQ/Gdl1r77kqkbeOGg8jWa3fHHkWzyBfBEZkv2yQ633RDCy9GPxD5RgVNPS5ajGp17s7thX56hwOtztAxOR5H7p5JvRmzTy3Yo13+IJ5IvIkKyudrgZ7GpMWfOt7Qnqty2YPBif6N51IvNf9xaKTO4k/t6rSji1daZFD1L54mqHIgvkiwgektuL1UhwwFvnSL3UzHgizu0Pqaa2FckLztSQv2H5Oy7vG+GVH9P3r1+ioF8xloaZep2vcVdOt39qarU9r1yDget8iy2QL1J8iX/Qr1/km/mSNbrgDjeELJAvUmxR41Ovnbg4k6I59ZNXBy7leqYrPtHt3tM/RbMbdSaw2728SIIURyBfpMgSU9orU0+yabGQMhpk8VAxNfLGQWL/qvFQoN1zBE81K7ZAvkixZT4SfK3f615ecHC3+xWWj9ONT40QP893kIn6EbnyfwFT4KGlcHSeyQAAAABJRU5ErkJggg==" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Complete the grouped frequency table for these data.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><img src="data:image/png;base64,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" alt></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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Estimate the mean and standard deviation of the heights of these 80 boys.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Explain briefly whether or not the normal distribution provides a suitable model for this population.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;"><img src="data:image/png;base64,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" alt> <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mu = 1.26,{\text{ }}\sigma = 0.133\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">no because the normal distribution is symmetric and these data are not <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The cumulative frequency graph below represents the weight in grams of 80 apples</span> <span style="font-family: times new roman,times; font-size: medium;">picked from a particular tree.</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Estimate the</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) median weight of the apples;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) 30<sup>th</sup> percentile of the weight of the apples.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Estimate the number of apples which weigh more than 110 grams.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) median = 104 grams <em><strong> A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Accept 105.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) 30</span><sup style="font-family: 'times new roman', times;">th</sup><span style="font-family: 'times new roman', times; font-size: medium;"> percentile = 90 grams </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>A1</strong></em></p>
<p><em style="font-family: 'times new roman', times; font-size: medium;"><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(80 − 49\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(= 31\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Accept answers 30 to 32.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On a very straightforward question there were many correct answers. However, there was evidence that some candidates had not previously encountered cumulative frequency graphs and hence scored low marks on the question.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On a very straightforward question there were many correct answers. However, there was evidence that some candidates had not previously encountered cumulative frequency graphs and hence scored low marks on the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>