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@genyrosk
Last active September 3, 2019 02:02
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tomayto-tomahto
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{
"cells": [
{
"cell_type": "code",
"execution_count": 287,
"metadata": {},
"outputs": [],
"source": [
"import os \n",
"import sys \n",
"import math \n",
"import numpy as np\n",
"import scipy.integrate as integrate\n",
"import matplotlib.pyplot as plt "
]
},
{
"cell_type": "code",
"execution_count": 288,
"metadata": {},
"outputs": [],
"source": [
"inf = 999"
]
},
{
"cell_type": "code",
"execution_count": 289,
"metadata": {},
"outputs": [],
"source": [
"def norm_pdf(x, mean=0.0, std=1.0):\n",
" return 1/math.sqrt(2*math.pi*std**2) * math.exp(-(x-mean)**2/(2*std**2))\n",
"\n",
"def norm_cdf(x, mean=0.0, std=1.0):\n",
" return integrate.quad(lambda x: norm_pdf(x, mean, std), -inf, x)[0]"
]
},
{
"cell_type": "code",
"execution_count": 290,
"metadata": {},
"outputs": [],
"source": [
"def get_axes():\n",
" fig, (ax1, ax2) = plt.subplots(1,2, figsize=(13,4))\n",
" ax1.spines['right'].set_visible(False)\n",
" ax1.spines['top'].set_visible(False)\n",
" ax2.spines['right'].set_visible(False)\n",
" ax2.spines['top'].set_visible(False)\n",
" return fig, (ax1, ax2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem\n",
"\n",
"> _Market research has indicated that customers are likely to bypass Roma tomatoes 🍅 that weigh less than 70 grams. A produce company produces Roma tomatoes that average 78.0 grams with a standard deviation of 5.2 grams._"
]
},
{
"cell_type": "code",
"execution_count": 291,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Tomato weight Cumulative Distribution Function')"
]
},
"execution_count": 291,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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6G1hF0Naxph/jrQS9rmwg2KGfJOh9JhGLwrg3hOuT6JXgw6nru1hPkNnnE9zk91V3XxsWNNcD/2NmRQRtcp+qNu9Kgh4g1hH01nBHgu0w470cxrDNDm7L+BTBgeXJ8ATgcP4zjHF7uA7vAmdWNYVy98eAe4BnLGh+sJAg8UnEqcD8cP97CrjO3Wu6cnE/cJId2v7/IYJ20fWq5agSXr28maBXkjyC7ymh5lNhIX0RcGz42Y0ENzBC7du96rP1/R2JqNxvpHLf3d8kqGW8OFzGdoIy7aVw/BKCbf02QfvxNxNcdm1uJLgJeRdBhxIv1jSRB/eW3Udwv9RWgu4+58VNcthyJpzHeoJtcBJxxxh3X0tw5f5nBOu7gaAsPNx52SvhPrMB+CHBPnF9LdOOJuh8oojge/8f//S5Er8guDF3t5nV+DydWjxMcPK+mSC5+H64LnWV448TXJnfaWY13ef1R4Kes94jaJazE6iridORSOh7r8W3CWJbQNBr050EvQXuItg354fb86D2/+GFsmkEFxB2hDF8JqxZaVasARMwaYXM7LvAVHefEnUsLYkFzVw2Ale6+yHVvS2FBVXq8wi6QKztRjQRSSIq90WSj2oIpF7MrL+ZnWJmKWFV980EN61J/VwF7G3hyUAqwVWcR5QMiCQvlfsiya+lP41Oml4bgmYrAwmq9f5B0GWeJMjMPiDo6vOLEYdyxMJq/40EfZzrKqFIclO5L5Lk1GRIRERERKQVS6jJkJlNNbOVFvRle0sN49uY2RPh+A8t6O8YM0s3s4fMbImZLTez/2jY8EVERERE5GjU2WQobCd8L0GvJXnAXDOb4e7L4ia7Ftjl7sPM7EqCx3t/gaAbxzbuPj7sKmyZmT0W3nVfo6lTp/rLL7985GskIpL8auu+r1XR8UJEpE4JHS8SqSGYCOSGXTWWEXQfNb3aNNMJuh+E4GFFk8L+Zh1ob2ZpBE+dKyN4umKttm+v7wNbRUSkNdLxQkSkYSSSEPTl4MdV53Ho49I/mcbdKwgegtGdIDnYT9B/70aCfnAPefKcmV1nZvPMbF5hYWG9V0JERERERI5MY3c7OpHg4U59CB7o8X0zO+TpeO5+v7tPcPcJWVlZjRySiIiIiIhUSSQh2Az0j3vfLxxW4zRh86DOBE9k+yLwsruXu/s2gic7TjjaoEVEREREpGEkkhDMBYab2WAzywCuJHgMebwZwJfD15cDsz3oz3QjcB6AmbUHTiF47LiIiIiIiDQDdSYE4T0BNwKzgOXAk+6eY2Z3mNm0cLIHgO5mlkvw5NKqrknvBTqYWQ5BYvE3d1/c0CshIiIiIiJHJqEnFbv7TGBmtWG3xb0uIehitPrn9tU0XEREWg8z+yvwGWCbu4+rYbwBvwUuAoqBr7j7x00bpYhI69XYNxWLiIg8CEw9zPgLgeHh33XAH5sgJhERCSVUQyDS2hSVlPP+mh2s3b6fisoYPTtlMmFgV4ZkdYg6NJEWx93fqnqCfS2mA38P7z37wMy6mFlvd9/aJAGKSKvg7pRXOqUVlZRWxCgpD/6XlscoqaiktDxGRSxGRcyJxfzg/+5UVDqV7lTGgr+qYR7OO1gGBEOqXgf/IRhe9boqntqm8U8n4rRhPThlSPdG3TZKCETi5O0q5p7ZuTzz8WbKKmOHjD+2X2duOm84k0b3JGjlICINoLbn3RySEJjZdQS1CAwYMKBJghOR5iUWc/YcKKdwXymFRcHf9n2lFO4rZe+BcvaWVFBUUkFRSfkn//eVVHCgvJKY1z3/5iY9NUUJgUhTcHce/Wgjd764jFgMPn9SPy45pg9j+nQiIy2FvF0HmLOykIfeX8/X/j6Pi8f35heXjaNLu4yoQxdpVdz9fuB+gAkTJrTAQ7uIJKIy5mzYsZ9VBfvYtLOYjeHfpp3F5O06UONFu4zUFDq1TadTZhodM9PomJlOdqdMOmWm0yEzjfYZqbRJT6VNWkrw98nrVNqkB8MyUlNISTHSUowUM1KrXscNS0s1UsNxqSn2yQVCMzDAzKi6ZBgMM+KvIVYNO+xnmviioxICafUqKmP85NmlPDFvE2cO78GvP3cMfbq0PWiaoVkdGJrVgX87dSB/fnstd72yiiWb9/DwtRMZ2L19RJGLJI1EnncjIkmqojLGivwi5m/YxdLNe1hZUMSqgiJKyj896e/cNp0B3doxuncnLhjTi16dMsnq2OaTvx4d2tApM02190dICYG0ahWVMW58dAEv5+Rz03nD+O75I0hJqb0wSU9N4VvnDOOUId259sG5fO6P7/P4dSczrGfHJoxaJOnMAG40s8eBk4E9un9AJHlVxpxFebuZs7KQuet3snDTborLKgHo3j6DUb07cvXJAxmZ3ZFR2R0Z2L09ndumRxx1clNCIK2Wu/Ofz+fwck4+t148mq+dOSThz54woCtPXX8aV/35A770wEc8863Tye6c2YjRirRcZvYYcA7Qw8zygNuBdAB3v4+gW+uLgFyCbke/Gk2kItJY9pdW8NryAl5fvo23Vxeyq7icFIPRvTtxxYn9OGFgV04c2JW+XdrqKn8ElBBIq3XfnLU89tFGvnXO0HolA1WG9ezA375yElfe/wH//uBcnvnWaWSmpzZCpCItm7tfVcd4B25oonBEpImUVlTyxoptvLBoK6+vKKCkPEaPDm04b1Qvzh6ZxZnDetC1ve7Faw6UEEir9NG6nfxm1go+c0xvfjhl5BHPZ1zfzvzuquP49wfncceLy/jlZeMbMEoREZGWZ9POYh77aCNPzN3Ejv1ldG+fwRUn9mfacX04cUDXwzbNlWgoIZBWZ3dxGTc/voAB3drxq88dc9RVk+eN6sU3zh7Cn+as5ZQh3Zl2bJ8GilRERKTlmL9hF398cw2vryjACI6PV58ygDOH9SAtVc/Cbc6UEEirc/uMHLbvK+WZb55OhzYN8xP4weSRfLRuJ7c9v5TThnanR4c2DTJfERGR5u79NTu4543VvJu7g67t0vnWOUP54skD6Vutxz5pvpQQSKsyZ1Uhzy/cws2ThjO+X+cGm296agr//bljuPh37/CzF5bx+6uOb7B5i4iINEcr84v4xczlvLWqkKyObfjJRaP54skDaN9AF9uk6egbk1bjQFkltz63hCFZ7fnWuUMbfP7De3XkxvOGcderq/js8X05d1TPBl+GiIhI1LbvK+V/X1nFE3M30jEznVsvHs01pwxUxxotmBICaTX+9NYaNu08wOPXnUKbtMYptK4/eyjPLdzMnS8t44zhPUhXm0kREUkS7s7TH2/mzheXsb+0gi+fNoibJw2nSzv1FNTS6WxFWoVtRSXc/9ZaLhqfzSlDujfacjLSUvjJRaNZW7ifRz7Y0GjLERERaUqbdhbzpb9+xA+eWsTwnh14+TtncvslY5UMJAnVEEircPerqymvjPGjKaMafVnnjerJGcN68H+vreazx/ejczs9XVFERFquZxfkceuzSwG4Y/pYrjl5oLoOTTIJ1RCY2VQzW2lmuWZ2Sw3j25jZE+H4D81sUDj8ajNbGPcXM7PjGnYVRA4vd1sRT8zdyNUnD2RQj/aNvjwz4ycXj2bPgXL+8s7aRl+eiIhIY9hfWsH3n1zEd59YxOjenZj13bP40qmDlAwkoToTAjNLBe4FLgTGAFeZ2Zhqk10L7HL3YcDdwK8B3P0f7n6cux8H/Buwzt0XNuQKiNTl/15bTbuMNL49aXiTLXN0705cPL43f3t3PbuLy5psuSIiIg1hbeE+pt3zDs8syOPb5w3j8etOoV/XdlGHJY0kkRqCiUCuu6919zLgcWB6tWmmAw+Fr/8JTLJDn/Z0VfhZkSaTu20fLy3ZypdOHUi3Jn48+s3nD2d/WQV/flu1BCIi0nLMWVXI9HvfZVdxOf+49mS+N3mkHiyW5BL5dvsCm+Le54XDapzG3SuAPUD1Oze/ADx2ZGGKHJk/vJFLZloq154xuMmXPaJXRy4e35sH313Pzv2qJRARkebN3fnL22v56t8+om+Xtjx/w+mcNqxH1GFJE2iSdM/MTgaK3X1pLeOvM7N5ZjavsLCwKUKSVmD99v08t3AzV588gO4RPTn45knD2V9Wyd/fXx/J8kVERBIRizm/nLmcn7+0nAvG9OLpb55G/25qItRaJJIQbAb6x73vFw6rcRozSwM6Azvixl/JYWoH3P1+d5/g7hOysrISiVukTn96ay1pqSlcd9aQyGIY3qsjk0b15O/vb6CkvDKyOERERGpTXhnjB/9cxJ/fXseXTx3IH68+UU8bbmUSSQjmAsPNbLCZZRCc3M+oNs0M4Mvh68uB2e7uAGaWAnwe3T8gTWjX/jKe+TiPy47rS89OmZHG8vWzhrBzfxnPfFw9jxYREYlWaUUl1z88n2c+3sz3LhjBT6eNVS9CrVCdCUF4T8CNwCxgOfCku+eY2R1mNi2c7AGgu5nlAt8D4rsmPQvY5O66s1KazKMfbaS0Isa/R3DvQHUnD+7G+L6d+cvba4nFPOpwREREgCAZ+OYjH/P6im3ceek4vj1pOIf2CSOtQUL1Qe4+E5hZbdhtca9LgCtq+eybwClHHqJI/ZRVxPj7++s5c3gPRmZ3jDoczIyvnzWEbz+2gNkrtnH+mF5RhyQiIq1caUUl33rkY2av2MYvLxvPF08eEHVIEiH1ISVJZ+aSrRTsLW0WtQNVLhqXTd8ubXngnXVRhyIiIq1cRWWMGx9dwOsrtvGLy8YpGRAlBJJ8/vruOoZktefs4c3nBvW01BSuPmUA76/dQe62fVGHIyIirZS78+Nnl/DqsgJ+Nm0sV588MOqQpBlQQiBJZUneHhbn7eErpzW/R6t/fkJ/0lONf3y4IepQRESklbrr1VU8OS+Pb08azpdPGxR1ONJMKCGQpPLoRxvITE/h0uOrPzsvej06tOHCcb15en4eB8rUBamIiDSth99fz+9n53LlSf357vnDow5HmhElBJI09pVW8PzCLVxyTB86ZaZHHU6NrjllIHtLKnhh0ZaoQxERkVbk9eUF3DYjh/NH9+Tnl45Tb0JyECUEkjRmLNxCcVklVzXjm6NOGtSVEb068IiaDYmISBNZXVDEzY8vZGyfTvz+qhNIS9XpnxxMe4QkjUc/2sCo7I4c379L1KHUysy4+uSBLM7bw9LNe6IOR0REktye4nK+/vd5ZKancv+/TaBtRmrUIUkzpIRAksKSvD0s3byXL548oNlXg156XF8yUlP45/y8qEMREZEkVlEZ48bHPmbz7gPcd80J9OnSNuqQpJlSQiBJ4bG5G8lMT2H6cc3vZuLqOrdL54KxvXhu4WZKK3RzsYiINI7fzFrJ26u38/NLxzFhULeow5FmTAmBtHgl5ZW8sGgLF47rTee2zfNm4uquOLEfu4vLmb18W9ShiIhIEpq9ooA/vbWWL548gC+c1HzvrZPmQQmBtHivL99GUUkFnz2h+dcOVDlzeBbZnTJ5Ss2GRESkgW3ZfYDvPbmI0b07cdtnxkQdjrQASgikxXvm4zyyO2Vy2tAeUYeSsNQU47Mn9OXNldvYtrck6nBERCRJlFfGuOmxBZRXxPjD1SeQma6biKVuSgikRdu+r5Q3VxVy6fF9SW1mTyauy+Un9iPm8MyCzVGHIiIiSeKuV1cxf8MufvnZ8Qzu0T7qcKSFUEIgLdqMhVuojHmLai5UZUhWByYM7MrT8/Nw96jDERGRFu7DtTu4b84arprYv0V0siHNhxICadGeWZDH+L6dGdGrY9ShHJFLj+/L6m37WJFfFHUoIo3KzKaa2UozyzWzW2oYP8DM3jCzBWa22MwuiiJOkZaqqKSc7z+1iAHd2nHrxbpvQOpHCYG0WCvzi1i6eW+LrB2octH43qSlGM8v3BJ1KCKNxsxSgXuBC4ExwFVmVv2M5VbgSXc/HrgS+EPTRinSsv38xeVs2X2Auz5/LO3bpEUdjrQwSgikxXpmQR5pKca0Y/tEHcoR69Y+g7NGZPHCoi3EYmo2JElrIpDr7mvdvQx4HJhebRoHOoWvOwPKkkUS9NqyAp6Yt4nrzx7KiQP1vAGpv4QSggSqetuY2RPh+A/NbFDcuGPM7H0zyzGzJWaW2XDhS2vl7ry4aCtnDu9B9w5tog7nqPvsQt0AACAASURBVEw7tg+bdx9g/sZdUYci0lj6Apvi3ueFw+L9FLjGzPKAmcBNNc3IzK4zs3lmNq+wsLAxYhVpUXbsK+WWZxYzuncnvnP+iKjDkRaqzoQgwarea4Fd7j4MuBv4dfjZNOAR4Hp3HwucA5Q3WPTSan28cTebdx/gkhZcO1DlgjG9yExP4fmF6m1IWrWrgAfdvR9wEfCwmR1yjHL3+919grtPyMrKavIgRZqbn72wjD0Hyrnr88eSkaaGH3JkEtlzEqnqnQ48FL7+JzDJzAyYDCx290UA7r7D3SsbJnRpzV5YtIWMtBQuGNMr6lCOWvs2aVwwJpuXFm+lvDIWdTgijWEz0D/ufb9wWLxrgScB3P19IBNoOQ8XEYnAGyu3MWPRFm44dxije3eq+wMitUgkIUikqveTady9AtgDdAdGAG5ms8zsYzP7UU0LUBWw1EdlzJm5ZCvnjsyiY2Z61OE0iOnH9mFXcTnvrN4edSgijWEuMNzMBptZBsFNwzOqTbMRmARgZqMJEgIdEERqsb+0glufXcqwnh345jlDow5HWrjGrltKA84Arg7/X2Zmk6pPpCpgqY+563eyraiUzxzT8psLVTlrRBad26ar2ZAkpfBC0Y3ALGA5QW9COWZ2h5lNCyf7PvB1M1sEPAZ8xfWADpFa3fXqKjbvPsCvPjueNml6GrEcnUT6pUqkqrdqmrzwvoHOwA6C2oS33H07gJnNBE4AXj/KuKUVe2HRFtqmpzJpdM+oQ2kwGWkpXDS+N88v3ExxWQXtMtRlnCQXd59JcLNw/LDb4l4vA05v6rhEWqJFm3bzt3fXcc0pA5gwSL0KydFLpIYgkareGcCXw9eXA7PDKzuzgPFm1i5MFM4GljVM6NIaVVTG+NfSfCaN7pl0J82XHNub4rJK3lypVhIiIlKzisoYtzyzhKyObfjR1FFRhyNJos6EIMGq3geA7maWC3wPuCX87C7gLoKkYiHwsbu/1PCrIa3Fe2t2sHN/WVI1F6oycVA3urfPYOaSrVGHIiIizdQjH2xg+da9/PSSsXRKkvvoJHoJXWJNoKq3BLiils8+QtD1qMhRe3HxFjq0SeOckcl3r0laagpTxmXz3ILNlJRXkpmuNqEiIvKp7ftK+d9XV3Hm8B5MHZcddTiSRNRhrbQYZRUxXl6az+QxvZL2ZPmicWo2JCIiNfvvl1dwoKyS2y8ZS9C7u0jDUEIgLcbbqwvZW1LBZ47tHXUojeaUId3o2i5dzYZEROQgCzbu4sl5eVx7xmCG9ewQdTiSZJQQSIsxc0k+nTLTOGNY8jUXqpKWmsKUsdm8vryAknI9w09ERCAWc26fkUPPjm24adLwqMORJKSEQFqE8soYr68o4PzRvZL+0ewXje/N/rJK3lqlZkMiIgJPztvE4rw9/OTi0XRok1w97EnzkNxnVpI0Plq3k93F5Uwem/w3UZ06tDtd2qXzr6X5UYciIiIR21tSzn/PWsnEQd2Ydmzy9bAnzYMSAmkRZuXkk5mewtkjkre5UJX01BQmj+nFa8sKKK1QsyERkdbsD2+sYVdxGbddMkY3EkujUUIgzV4s5rySU8BZw7Nom5GcvQtVd9H43hSVVvDO6u1RhyIiIhHJ21XMX99dx2XH92Vc385RhyNJTAmBNHuLN+8hf28JU1pBc6Eqpw3tQafMNF5Sb0MiIq3W/8xaiQE/mDwy6lAkySkhkGZvVk4+qSnGpNE9ow6lyWSkpTB5bDavLiugrCIWdTgiItLEFuft5rmFW/jamYPp06Vt1OFIklNCIM3erJx8ThnSjS7tMqIOpUlNHZtNUUkFH6zdEXUoIiLShNydX7y0nO7tM7j+7KFRhyOtgBICadZytxWxtnB/q2ouVOWM4T1ol5HKrBz1NiQi0pq8tnwbH67byXcuGEHHzPSow5FWQAmBNGuzcgoAmDym9SUEmempnDMyi1eXFRCLedThiIhIEyivjPFf/1rO0Kz2XHlS/6jDkVZCCYE0a7Ny8jmufxeyO2dGHUokpozNZltRKQs27Y46FBERaQL/nJ/H2sL93HLhaNJTdZomTUN7mjRbm3cfYHHenlbZXKjKOSN7kpZivKJmQyIiSa+kvJLfvraa4wd04fxW1JGGRE8JgTRbVSfBU8b2ijiS6HRum86pQ7szKycfdzUbEhFJZo98sIH8vSX8cMpIPYRMmpQSAmm2ZuXkM7xnB4ZkdYg6lEhNGZvN+h3FrN62L+pQRESkkewrreCPb67hjGE9OG1oj6jDkVZGCYE0Szv3l/HRup2turlQlcljemEGs5aq2ZCISLL62zvr2LG/jB9M0UPIpOkllBCY2VQzW2lmuWZ2Sw3j25jZE+H4D81sUDh8kJkdMLOF4d99DRu+JKvXlhcQc5QQAD07ZXJ8/y7MWqaEQEQkGe0uLuP+t9YyeUwvjuvfJepwpBWqMyEws1TgXuBCYAxwlZmNqTbZtcAudx8G3A38Om7cGnc/Lvy7voHiliT3Sk4+fbu0ZVzfTlGH0ixMGZvN0s17ydtVHHUoIiLSwO6bs5Z9ZRV8f7JqByQaidQQTARy3X2tu5cBjwPTq00zHXgofP1PYJLpbhg5QvtLK3hr9XYuGNNLN1WFJoc1Ja+Ez2UQEZHksG1vCQ++t47px/ZhZHbHqMORViqRhKAvsCnufV44rMZp3L0C2AN0D8cNNrMFZjbHzM6saQFmdp2ZzTOzeYWFhfVaAUk+c1YVUlYRU3OhOIN7tGdErw56arGISJK5941cKiqd75w/IupQpBVr7JuKtwID3P144HvAo2Z2SBsQd7/f3Se4+4SsrKxGDkmau1k5+XRrn8FJg7pGHUqzMmVsNnPX72THvtKoQxERkQawdc8BHvtoE1dM6M+gHu2jDkdasUQSgs1A/LOz+4XDapzGzNKAzsAOdy919x0A7j4fWAMoBZZalVXEmL18G+eP7kmantB4kCljs4k5vL58W9ShiIhIA7j/rbXE3PnWOUOjDkVauUTOuOYCw81ssJllAFcCM6pNMwP4cvj6cmC2u7uZZYU3JWNmQ4DhwNqGCV2S0XtrtlNUWqHmQjUY26cTfbu05RX1NiQi0uIVFpXy2EcbufT4vvTv1i7qcKSVqzMhCO8JuBGYBSwHnnT3HDO7w8ymhZM9AHQ3s1yCpkFVXZOeBSw2s4UENxtf7+47G3olJHnMyimgfUYqpw/TQ1mqMzMmj+3FW6u3s7+0IupwRETkKDzwzjpKK2KqHZBmIS2Ridx9JjCz2rDb4l6XAFfU8LmngaePMkZpJSpjzqvLCjhnZE8y01OjDqdZmjI2m7+9u545qwq5aHzvqMMREZEjsLu4jIffX89njunDkKwOUYcjoicVS/OxYOMutu8rZfLYXlGH0mxNGNiVbu0z1NuQiEgL9uB769lfVskN56p2QJoHJQTSbMzKySc91Th3VM+oQ2m20lJTmDSqJ7OXb6OsIhZ1OCIJq+uJ9+E0nzezZWaWY2aPNnWMIk2hqKScv727ngvG9GJUth6+Kc2DEgJpFtydWTkFnDa0B50y06MOp1mbMjabotIK3l+7I+pQRBKSyBPvzWw48B/A6e4+FvhOkwcq0gQe+WAjew6Uc+O5w6IOReQTSgikWViRX8TGncXqXSgBZwzvQbuMVDUbkpYkkSfefx241913Abi7+teVpHOgrJK/vL2Ws0ZkcWz/LlGHI/IJJQTSLMzKyccMLhij+wfqkpmeyjkjs3h1WQGxmEcdjkgiEnni/QhghJm9a2YfmNnUmmakJ9tLS/b43I3s2F/GTeepdkCaFyUE0iy8vDSfCQO7ktWxTdShtAhTxmZTWFTKgk27og5FpKGkETyr5hzgKuDPZnbIJVQ92V5aqtKKSv40Zy0TB3fjpEHdog5H5CBKCCRyG3cUsyK/SM2F6uHcUT1JTzVm5RREHYpIIhJ54n0eMMPdy919HbCKIEEQSQpPz99M/t4S1Q5Is6SEQCJX1RZeCUHiOmWmc9rQHszKycddzYak2UvkiffPEdQOYGY9CJoQ6cn2khQqKmP8cU4ux/bvwhl68KY0Q0oIJHKzcvIZ3buTHt1eT1PGZrNhRzErC4qiDkXksBJ84v0sYIeZLQPeAH7o7upKS5LCjEVb2LTzADedOwwzizockUMoIZBIFRaVMn/jLqboYWT1dsGYXpjBrKVqNiTNn7vPdPcR7j7U3X8RDrvN3WeEr93dv+fuY9x9vLs/Hm3EIg2jMubc+0Yuo7I7Mmm0nrMjzZMSAonUq8sKcFdzoSOR1bENJw7oysvqflREpNl6eWk+awr3c+N5qh2Q5ksJgURqVk4+A7q1Y1R2x6hDaZGmjM1m+da9bNpZHHUoIiJSjbtzzxu5DMlqz4XjekcdjkitlBBIZPaWlPPemu1MHZetqyZHqKpmRQ8pExFpfmav2MbyrXu54ZxhpKboOCfNlxICicwbK7ZRXulqLnQUBnQPaleUEIiINC/uzu9n59K/W1umHdcn6nBEDksJgUTm5aX59OzYhuP1+PajMmVsNvM27KKwqDTqUEREJPRu7g4WbtrN9WcPJT1Vp1vSvGkPlUiUlFfy5spCJo/tRYqqUY/KlLHZuMNry9XbkIhIc/H72avp1akNl5/YL+pQROqkhEAi8daqQg6UVzJ1rG6yOlqje3ekf7e2ajYkItJMzF2/kw/X7eQbZw2lTVpq1OGI1CmhhMDMpprZSjPLNbNbahjfxsyeCMd/aGaDqo0fYGb7zOwHDRO2tHQv5+TTuW06Jw/pFnUoLZ6ZMWVMNu/l7qCopDzqcEREWr17ZufSvX0GV00cEHUoIgmpMyEws1TgXuBCYAxwlZmNqTbZtcAudx8G3A38utr4u4B/HX24kgzKK2O8vnwbk0b3VLvKBjJlXDZllTHeWFkYdSgiIq3a4rzdzFlVyLVnDqZthmoHpGVI5GxsIpDr7mvdvQx4HJhebZrpwEPh638CkyzsR9LMLgXWATkNE7K0dB+u3cmeA+VMVe9CDeaEAV3p0SFDzYZERCJ2z+xcOmWm8W+nDIw6FJGEJZIQ9AU2xb3PC4fVOI27VwB7gO5m1gH4f8DPDrcAM7vOzOaZ2bzCQl3hTHYv52ylbXoqZ43IijqUpJGaYlwwphdvrthGSXll1OGIiLRKK/L38sqyAr56+mA6ZqZHHY5Iwhq7vcZPgbvdfd/hJnL3+919grtPyMrSSWIyi8WcV3IKOGdkFpnpqkptSFPGZrO/rJL31myPOhQRkVbpD2+soX1GKl89fVDUoYjUSyIJwWagf9z7fuGwGqcxszSgM7ADOBn4bzNbD3wH+LGZ3XiUMUsLtmDTbrYVlephZI3gtKE96NgmjVlL1f2oiEhTW1u4jxcXb+GaUwfSpV1G1OGI1EtaAtPMBYab2WCCE/8rgS9Wm2YG8GXgfeByYLa7O3Bm1QRm9lNgn7vf0wBxSws1Kyef9FTj3FE9ow4l6WSkpXDuqJ68tryAypiTquc7iIg0mT++uYb01BS+dsaQqEMRqbc6awjCewJuBGYBy4En3T3HzO4ws2nhZA8Q3DOQC3wPOKRrUhF3Z1ZOPqcN7UHntmpb2RimjM1mx/4y5q3fGXUoIiKtRt6uYp5dsJmrJg4gq2ObqMMRqbdEaghw95nAzGrDbot7XQJcUcc8fnoE8UkSWZFfxIYdxXzjrKFRh5K0zhmZRUZaCrNyCjh5SPeowxERaRX+NGctZvCNs1U7IC2TOoGXJjMrJx8zuGBMr6hDSVrt26Rx5rAezMrJJ2i1JyIijalgbwlPzNvE5Sf2o3fntlGHI3JElBBIk3l5aT4nDeym6tRGNmVsNpt3HyBny96oQxERSXp/fmstlTHnm2cPizoUkSOmhECaxLrt+1mRX8TksaodaGznj+lFaorxr6Vbow5FRCSp7dxfxj8+3Mj0Y/swoHu7qMMROWJKCKRJzFwSnJxeNL53xJEkv27tMzh1SHdmLlGzIRGRxvTXd9ZRUlHJt87VvXHSsikhkCbx4uKtnDiwK326qH1lU7j4mN6s276fZVvVbEhEpDHsOVDOQ++t56JxvRnWs2PU4YgcFSUE0ujWFu5j+da9qh1oQlPGZpOaYry0WM2GREQaw9/fW09RaYVqByQpKCGQRvdpcyE9nbipdGufwWlDu/PSkq1qNiQi0sD2l1bwwLvrmDSqJ2P7dI46HJGjpoRAGt2Li7cyYWBXdcfWxC4e35sNO4rV25CISAN79MON7C4u54bz1LOQJAclBNKo1hTuY0V+kZoLReCTZkNL1GxIRKShlJRXcv/bazljWA9OGNA16nBEGoQSAmlUMxerd6GodG2fwenDevDSYjUbEhFpKE/O20RhUSk3nKvaAUkeSgikUb20ZCsnDepKdufMqENplS4en83GncUs3axmQyIiR6usIsZ9b65hwsCunDKkW9ThiDQYJQTSaHK3qblQ1CaPySZNzYZERBrE0x/nsWVPCTdNGo6ZRR2OSINRQiCNZuaSrZjBheOUEETlk2ZDS7ao2ZCIyFEor4zxhzdzObZfZ84a3iPqcEQalBICaTQvhb0LqblQtC4+pjebdh5gyeY9UYciItJiPb9wC5t2HuCm81Q7IMlHCYE0itxtRawsKOJiNReK3OQxvYJmQ3pImYjIEamMOX94I5cxvTsxaXTPqMMRaXBKCKRRPL9wCymm3oWagy7tMjhjeA9eVG9DEiEzm2pmK80s18xuOcx0nzMzN7MJTRmfyOG8uHgLa7fv56bzhql2QJJSQglBXQW5mbUxsyfC8R+a2aBw+EQzWxj+LTKzyxo2fGmO3J3nF27h9GE96NlJzYWag2nH9mHz7gPM37Ar6lCkFTKzVOBe4EJgDHCVmY2pYbqOwM3Ah00boUjtYjHnntm5jOjVgSljs6MOR6RR1JkQJFiQXwvscvdhwN3Ar8PhS4EJ7n4cMBX4k5mlNVTw0jwt2LSbjTuLmXZsn6hDkdDksdlkpqfw7ILNUYcirdNEINfd17p7GfA4ML2G6e4kOH6UNGVwIofzck4+q7ft48bzhpOSotoBSU6J1BAkUpBPBx4KX/8TmGRm5u7F7l4RDs8E1F6hFXh+wWbapKUwdZyupDQXHdqkMXlMNi8t2UpZRSzqcKT16QtsinufFw77hJmdAPR395cONyMzu87M5pnZvMLCwoaPVCSOu/P72bkMyWqve+IkqSWSENRZkMdPEyYAe4DuAGZ2spnlAEuA6+MSBElC5ZUxXly8lfNH96JjZnrU4UicS4/vw+7icuas0kmUNC9mlgLcBXy/rmnd/X53n+DuE7Kysho/OGnVXlu+jeVb93LDOcNIVe2AJLFGv6nY3T9097HAScB/mNkhjcp1xSd5vJu7nR37y5h+nJoLNTdnDs+iW/sMnluoZkPS5DYD/ePe9wuHVekIjAPeNLP1wCnADN1YLFEKagdWM6BbOx3TJOklkhDUVZAfNE14j0BnYEf8BO6+HNhHUOhTbZyu+CSJ5xduoVNmGmeP1PfY3KSnpvCZY3rz2rICikrKow5HWpe5wHAzG2xmGcCVwIyqke6+x917uPsgdx8EfABMc/d50YQrAnNWFbI4bw/fOmcoaanqlFGSWyJ7+GEL8tAM4Mvh68uB2e7u4WfSAMxsIDAKWN8gkUuzU1xWwaycfC4+pjdt0lKjDkdqcOnxfSmtiPHy0vyoQ5FWJGwqeiMwC1gOPOnuOWZ2h5lNizY6kUO5O799fTV9u7Tlsyf0izockUZXZ48/7l5hZlUFeSrw16qCHJjn7jOAB4CHzSwX2EmQNACcAdxiZuVADPiWu29vjBWR6L22fBvFZZVMP676LSbSXBzfvwsDu7fj+YVbuGJC/7o/INJA3H0mMLPasNtqmfacpohJpDZvrixkwcbd/PKy8WSkqXZAkl9CXYDWVZC7ewlwRQ2fexh4+ChjlBbi+QWb6d05k4mDukUditTCzJh+XF9+P3s1BXtL6KXnRIiIHMTduevVVfTv1pYrJqh2QFoHpb3SILYVlfDmqkKmH9dX/TQ3c5ce1wd3eGHRlqhDERFpdl5dVsCSzXu46bzhpOveAWkltKdLg3huwWYqY87lJ+pqSnM3JKsDx/brzNMfq7chEZF4sVhQOzC4R3s+e7yav0rroYRAjpq789S8PI4f0IVhPTtEHY4k4PIT+7F8616Wbt4TdSgiIs3Gv5bmsyK/iJsnDVfPQtKqaG+Xo7Y4bw+rt+3jihN1k2pLMe3YvmSkpfDUvE11Tywi0gpUxpy7X1vF8J4duORYPXdAWhclBHLUnpq/icz0FD5zrB7r3lJ0bpfO1LHZPLdwCyXllVGHIyISuRcWbSF32z6+c/4IPZVYWh0lBHJUSsormbFwC1PHZtMpMz3qcKQePj+hP3sOlPPqsoKoQxERiVRFZYzfvr6aUdkduXBcdtThiDQ5JQRyVF5ZVsDekgr1ad8CnTa0O327tOVJNRsSkVbumQWbWbd9P9+7YIR6ypNWSQmBHJWn5m2ib5e2nDqke9ShSD2lpBiXn9iPd3K3k7erOOpwREQiUVJeyf+9uopj+nXmgjG9og5HJBJKCOSIbd59gHdyt/O5E/TsgZaqqpvYp+erC1IRaZ0efn8DW/aUcMuFozDTsUxaJyUEcsSe+GgjgJoLtWD9u7Xj9KE9eGr+JmIxjzocEZEmtedAOfe8kcvZI7I4bWiPqMMRiYwSAjki5ZUxHp+7iXNGZNG/W7uow5Gj8PmT+pO36wBv526POhQRkSZ135w17DlQzo+mjow6FJFIKSGQI/L68gK2FZVy9ckDow5FjtKUsb3o0SGDh9/fEHUoIiJNJn9PCX99Zx2XHteHsX06Rx2OSKSUEMgR+ceHG+nTOZNzR/WMOhQ5Sm3SUvnCSf2ZvaKAzbsPRB2OiEiT+O3rq4i58/3Jqh0QUUIg9bZ++37eXr2dKycO0MNbksRVEwcA8NiHGyOORESk8eVu28cTczdxzSkD1exVBCUEcgQe+2gjqSnGF07SzcTJol/Xdpw3qhePz91IWUUs6nBERBrVr19eQbuMNG48d1jUoYg0C0oIpF5Kyit5an4eF4zuRa9OmVGHIw3o304dyPZ9Zbyckx91KCIijea93O28uqyAb54zlO4d2kQdjkizoIRA6uWFRVvYub+Ma07RzcTJ5sxhPRjYvR2P6OZiEUlSlTHnjheX0bdLW649Y3DU4Yg0GwklBGY21cxWmlmumd1Sw/g2ZvZEOP5DMxsUDr/AzOab2ZLw/3kNG740JXfngXfWMbJXR04fpicTJ5uUFOPqkwfw0fqdrMjfG3U4IiIN7om5m1iRX8SPLxpNZnpq1OGINBt1JgRmlgrcC1wIjAGuMrMx1Sa7Ftjl7sOAu4Ffh8O3A5e4+3jgy8DDDRW4NL331+5gRX4R/37GID3NMUldcWJ/MtNT+Ns766MORUSkQe0tKed/X1nJxEHduGh8dtThiDQridQQTARy3X2tu5cBjwPTq00zHXgofP1PYJKZmbsvcPct4fAcoK2ZqcFeC/XXd9bTrX0G04/rG3Uo0ki6ts/gcyf049kFmyksKo06HBGRBnPP7Fx2Fpfxn58Zo4taItUkkhD0BTbFvc8Lh9U4jbtXAHuA6m1KPgd87O6HnGWY2XVmNs/M5hUWFiYauzSh9dv38/qKAq45eYCqWZPctWcMpjwW4+H310cdiohIg1i/fT9/e3cdl5/Qj/H99BAykeqa5KZiMxtL0IzoGzWNd/f73X2Cu0/IyspqipCknh58bz1pKaabiVuBIVkdOH90Lx7+YAMHyiqjDkdE5Kjd+eIyMlJT+OEUPYRMpCaJJASbgfgO5/uFw2qcxszSgM7AjvB9P+BZ4EvuvuZoA5amt+dAOU/O28Qlx/ahp7oabRW+fuYQdhWX8/THeVGHIiJyVF7Jyef1Fdv49qThOoaJ1CKRhGAuMNzMBptZBnAlMKPaNDMIbhoGuByY7e5uZl2Al4Bb3P3dhgpamtbD76+nuKySr50xJOpQpImcNKgrx/brzAPvrCMW86jDERE5IsVlFfzshWWM6NWBf1c3oyK1qjMhCO8JuBGYBSwHnnT3HDO7w8ymhZM9AHQ3s1zge0BV16Q3AsOA28xsYfjXs8HXQhpNcVkFf313PeeN6smYPp2iDkeaiJnxtTOHsG77fl5dXhB1OCIiR+R3r+eyefcBfn7peNJT9eglkdqkJTKRu88EZlYbdlvc6xLgiho+93Pg50cZo0To8Y82sXN/GTecOzTqUKSJXTgum4Hd23HvG7lMHtNLvXKISIuyuqCIv7y9lstP7MfEwd2iDkekWVO6LLUqq4hx/1trmTi4GycOVGHa2qSlpnDDOcNYnLeHN1ep9y8RaTncnVufW0r7Nmn8x4Wjog5HpNlTQiC1enZBHvl7S7jh3GFRhyIRueyEvvTt0pbfvrYad91LICItw1Pz8/hw3U5+NHUk3Tvo8UcidVFCIDUqr4zxhzfXMK5vJ84a3iPqcCQi6akpfOvcoSzctJt3crdHHY6ISJ0K9pZw54vLmDioG1edNCDqcERaBCUEUqOn5+exYUcx35k0Qm3HW7nLT+xH786Z/O511RLIkTOzqWa20sxyzeyWGsZ/z8yWmdliM3vdzPTQE6k3d+cnzy6hrCLGry8/hpQUHb9EEqGEQA5RWlHJ715fzbH9uzBptDqFau3apKXyzXOGMnf9Lt5fsyPqcKQFMrNU4F7gQmAMcJWZjak22QJggrsfA/wT+O+mjVKSwYxFW3ht+TZ+OGUkg3u0jzockRZDCYEc4rEPN7JlTwk/nDxStQMCwOcn9Kd350x+PWulagnkSEwEct19rbuXAY8D0+MncPc33L04fPsBwUMwRRJWWFTK7TNyOK5/F756up45IFIfSgjkIAfKKrnnjTWcPLgbpw/rHnU40kxkpqfy3QtGsGjTbl5emh91ONLy9AU2xb3PC4fVk5VhiQAAFwVJREFU5lrgXzWNMLPrzGyemc0rLFTvVxJwd26fsZTi0kp+c/kxpKqpkEi9KCGQgzz43nq27yvlB1NUOyAH+9wJ/RjRqwO/mbWSispY1OFIkjKza4AJwG9qGu/u97v7BHefkJWV1bTBSbP1zMebmbkkn+9eMILhvTpGHY5Ii6OEQD6xfV8p976Ry6RRPTlpkJ47IAdLTTF+NGUUa7fv58l5eVGHIy3LZqB/3Pt+4bCDmNn5wE+Aae5e2kSxSQu3Ycd+bnt+KScP7sZ1Zw2JOhyRFkkJgXzirldXUVJeyY8vHh11KNJMTRrdkwkDu3L3a6vYX1oRdTjScswFhpvZYDPLAK4EZsRPYGbHA38iSAa2RRCjtEAVlTG+88RCUlKMu75wnJoKiRwhJQQCwIr8vTz+0UauOWUgQ7M6RB2ONFNmxo8vHk1hUVCbJJIId68AbgRmAcuBJ909x8zuMLNp4WS/AToAT5nZQjObUcvsRD7x+9m5LNi4m19eNp6+XdpGHY5Ii5UWdQASPXfnFy8t///t3Xl8VOW9x/HPb2ayJxAIBJJAMEAAWWQxslhrrVqLS0Vpq2BV2tra9ta23urt9b56u9He2r7aW+9FrUrVC21vxa31UuvWihVbXIgi+x7AEMIOCSHbLM/9YwYIKQyjhJxJ5vt+veZ1zjzzZPjx5GR+8zvnOeeQl5nG7ZeWex2OJLkJpb2YPqGEX71WxacrBurSfpIQ59xzwHPt2r7bZv3STg9KurQ3qvZx76KNTJ9QwifGFnsdjkiXpiMEwktrdvHaxr1845Jy8rPTvQ5HuoC7Lh9BRsDP7D+u9joUEUlBu+ubue13yzirTw4/uHqU1+GIdHkqCFJcQ0uI7y9czYj+edw0RTcGlcQU5mVy+6XlvLJ+Dy+v3eV1OCKSQoLhCLf9bhmHW0I8eOO55GWmeR2SSJengiDF/eKlDeysb+bH08eQ5tfmIImbdf5ZDC3M5XsLV+sEYxHpND97cT1vbd3P3dPHMEyXGBXpEPoGmMJWbq9j3pIt3DhpEBNKe3kdjnQxaX4fP752DNsPNPGzF9d7HY6IpIDnVtYyd3EVN08ZxDXj493bTkTeDxUEKSoYjvBvf1hBQW4G/zJ1uNfhSBc1saw3s6YMYv7rW6ncut/rcESkG1ux/SDffOJdJpTm821dHlukQyVUEJjZVDNbb2abzOyuE7yeYWaPx15/08zOirUXmNkrZtZgZvd1bOhyOu5dtIlVNfX8cNooemj+pZyGb00dQXHPLL719Aqag2GvwxGRbmjHwSZumV9Jn9wM5t5cQUbA73VIIt3KKQsCM/MD9wOXAyOBmWY2sl23W4ADzrmhwD3AT2PtzcB3gDs7LGI5be+8d4D7X9nE9AklTB1d5HU40sXlZAS4e/oYqvYc5ueaOiQiHexwS4gvzK+kqTXMo589jz65GV6HJNLtJHKEYCKwyTlX5ZxrBRYA09r1mQbMj60/BVxiZuacO+yc+xvRwkCSQGNriG8+/i79e2TyfV2qTTrIhcP6cuPkUh7+2xb+ul43mRWRjhEMR/jaY8tYt7Oe+24Yr5OIRc6QRAqCEqC6zfPtsbYT9ondkbIOKEg0CDO71cwqzaxyz549if6YfACz/7iGbfsb+fmnx2qqkHSof79yJCP653Hnk8vZfUj7AETk9EQijm89tYJF63Yze9poLhpe6HVIIt1WUpxU7Jyb65yrcM5V9O3b1+twuq0nKqtZsLSaL39kCFOGJFyviSQkM83PvTPH09AS4o4nlhOJOK9DEpEuyjnH7GfX8IdlNdx52TBunKz75IicSYkUBDXAwDbPB8TaTtjHzAJAT2BfRwQoHWP1jjq+88wqzh9SwB0fG+Z1ONJNlffL47tXjeK1jXv5r79s8DocEemCnHPc8+cNzFuylVsuKOOrHx3qdUgi3V4iBcFSoNzMyswsHZgBLGzXZyEwK7b+KWCRc067B5NEXWOQr/z2HXplpzNn5ngCugGZnEEzJw7kuooBzFm0iT+tqPU6HBHpQpxz/OdLG5izaBPXVQzg21ecjZl5HZZItxc4VQfnXMjMbgNeBPzAo8651WY2G6h0zi0EHgF+Y2abgP1EiwYAzGwr0ANIN7NrgMucc2s6/r8iJ9IaivDl375NbV0TC26doqszyBlnZvzwmtFs3nOYO59cTlmfHEYW9/A6LBFJcs45fvLCOh56tYoZ5w3kx9eOwedTMSDSGSzZduRXVFS4yspKr8PoFpxz3PHkcn7/Tg33XD+Wa8cP8DokSSG7DzUz7b6/Y8DT/3Q+RT2zvA6pO9G3JJQvupNIJHrOwLwlW7lxcimzrx6tYkCkYyT0h6S5I93YPX/ZyO/fqeGfLx2mYkA6XWFeJg/PquBQc4ibH3mLA4dbvQ5JRJJQczDM1x5bxrwlW/n8h8r44TQVAyKdTQVBN/Xgq5uZ8/JGPn3uAL5+iU7IEm+MKu7Jr2ZVsG1/I5+bt5TDLSGvQxKRJHKwsZWbHnmTP62s5dtXnM13rtI5AyJeUEHQDT3yty385Pl1fGJsMT/55Dn6cBVPTR5cwL0zx7Ni+0E+P28pDSoKRATYuOsQ03+5hOXVdcyZOZ4vXjhY+UrEIyoIupmHX6vih8+uYeqo/vziurH4ddhVksDHR/XnnuvHUbntADc98iZ1TUGvQxIRDz2/spZr7v879c1BfvuFSVw9ttjrkERSmgqCbsI5x93Pr+VHf1rL5aP7M2fmeNJ0eVFJItPGlXD/DRNYVVPHDb96g70NLV6HJCKdrDUU4e7n1vKV/32H8n55PPu1DzOxrLfXYYmkPH1j7AZaQxHufHIFD71axU2TB3HfDRNID+hXK8ln6uj+zL25gs17Gph2399Zt7Pe65BEpJNs2t3A9Af+zkOLq/jMpFIe/9Jk+vfM9DosEUEFQZe3s66Z6+e+ztPvbOebHxvG7GmjNE1IktpHhxfyxJemEIpE+OQvl7Bo3S6vQxKRMygcccxfspWr7n2NmgNNPHTTufzHtWPICPi9Dk1EYlQQdGFvVO3jqntfY8POQ/zyMxP4+iXlOiFLuoRzBuTzf1+9gLK+Odwyv5KfvrCOYDjidVgi0sFW76hj+gNL+N7C1UwsK+DF2y/k46P6ex2WiLRzyjsVS/JpCYX5xZ83MHdxFWUFOTz2xcmU98vzOiyR96V/z0ye/NL5zH52DQ/8dTNvVO1jzozxDOyd7XVoInKa6hqDzFm0kXlLttIrO43/un4c08YVa6eVSJJSQdDFrNxex788tZx1Ow8xc+JAvn3lSHIz9GuUrikr3c/d08dwwdA+3PX0Ci67ZzF3XDaMz55/FgGdFC/S5TQHw8xfspX7X9nEoZYQM84r5a6pI+iZneZ1aCISh75JdhH7D7fysxfXs2Dpe/TJzeDRz1Zw8Yh+Xocl0iGuPKeIcaX5fPeZVfzoT2t55t0afnD1KM4dpKuPiHQFTa1hnny7mgf/upkddc1cNLwv/zp1BGcX9fA6NBFJgAqCJNfQEmL+kq3MXVxFQ0uIz3+ojG9cWk6PTO1tke6lJD+Lh2dV8PyqnXx/4Wo++cDrXDayH9+aOpyhhZoSJ5KMDhxu5TdvbGPekq3sP9zKhNJ8fn7dWM4f0sfr0ETkfVBBkKTqGoP871vb+NXiKg40Brl4RCF3XT6CYTpXQLoxM+OKMUVcNLwvj/5tCw++WsVl9yzmqnOK+eKHBzNmQE+vQxRJec45Xq/ax4K3qnlh1U5awxEuHlHIlz8yhPPO6qXzBES6IBUESWZtbT2/fn0bzyyroSkY5qLhfbn90mGMG5jvdWginSY7PcBtF5dzw6RBPPjqZn735nssXL6DyYN7c+PkQVx6dj8y03TJQpHO4pxjbe0hnl9Vyx+X72DrvkZ6ZAa4YVIpN0wq1c4qkS7OnHNex3CciooKV1lZ6XUYnap6fyPPrqhl4fIdrK2tJzPNxzXjSrhpyiBGFWuPqEh9c5DH36pm3pKt1BxsokdmgE+MLWbauBImlOan4gnI2gVLauaLztQcDPP2tgMs3riHl1bvYsvew/gMJpUV8OmKAVwxpkiFuUjySyhfqCDwQGsocvRD9tX1e1hTG71b64TSfD4xtphrx5eQn53ucZQiyScccby+eR9PvV3NC6t30hyM0Cs7jY8OL+SjIwqZNLg3hXkpcedTFQSkRr7oTA0tIVZur+Pd6oO8XrWPt7bsozkYIeAzJg3uzRVjivj4qP70yc3wOlQRSVxC+UJThs4w5xw76ppZUX2Qd6sPsqz6ICu319EUDBPwGecO6sW/Th3BVecU6frrIqfg9xkXlPfhgvI+HGoOsnjDXv6ydheL1u/m98tqABjcJ4eJZb0ZOzCfkUU9GN4/T3sxRdpwzrGzvpmNuxrYuLuB9TvrWV5dx8bdh4jE9hEOLcxlxnmlfLi8D5MGF+jy1iLdXEJ/4WY2FfhvwA887Jz7SbvXM4BfA+cC+4DrnXNbY6/9G3ALEAa+7px7scOiTxKhcITdh1qorWtix8Fm3tvfyObdDWza08Dm3Q0cbg0DkO73cXZxD64/byDnDylgypAC8nS1IJEPJC8zjSvPKeLKc4oIhSOsqKlj6Zb9LN26n+dW1rJgaTUAPoOyPjkM65dHaUE2pb2PPfr3zCQjoGKhM5xOHpH3pzUU4WBjK7vqW6g52MSOg03HLav2HKahJXS0f++cdMaU9GTq6P6MK81n3IB8euXoKLVIKjnllCEz8wMbgI8B24GlwEzn3Jo2ff4JOMc592UzmwFc65y73sxGAo8BE4Fi4C/AMOdc+GT/XmcdAo5EHGHnCEccwXCEpmCY5tbosikYpqk1TFMwRFOsrb4pyMHGVg42BTnQGFtvDLK3oYVd9c1H96oc0b9HJkMLcxlamMuQwlxGF/dgZHEPffkQ6QSRiKP6QCNra+tZU3uItbX1bN7TwPb9TbSGI8f1zcsM0Dcvgz65GfTNzaB3Tjp5mQHyMtPIzQyQlxEgNyNAXmaArHQ/GQE/6QEfGQHf0WVGwE+a3zrz6ipdasrQ6eSReO/bVacMOecIhh2hSIRgyBGMRAiGI4TCjtbYMhiOtjUHIzS2hmhsDdPYGuJwS2zZGqaxJURDS5gDja3sP9waXTa0cqjNl/0jstL8FOdnUpyfxZC+0bxUHnsUaAqQSHfWYVOGJgKbnHNVAGa2AJgGrGnTZxrw/dj6U8B9Fs2M04AFzrkWYIuZbYq93+uJBPd+PP32dn75102EI45QxB1dRo57Hjna/kFOnTCDHplp9MpOIz87nYLcdIb1y6M4P5OinlkU5WdS1DOTkvws7fkX8ZDPZwwqyGFQQQ5TRxcdbY9EHLsONbNtXyPv7WtkV30zexta2NvQyp6GFtburGf/4VYONYcIt6/yE5Ae8BHwGX4zfD7D7zN8Zvh9EPD58Pk4+lp5YS4P3VTRkf/tZPaB84g7Aye63b5gGStr6nCAc9Ev6EfXcbG2aF/nHJG27Rx5re3z6M9HItEl7drbvu+RHHS60vxGdnq0WO2Vk0av7HQGFWTTKzudgpx0euWk0zcvg5L8LErys8jPTtPlQEXkpBIpCEqA6jbPtwOTTtbHORcyszqgINb+RrufLWn/D5jZrcCtAKWlpYnGfpxeOWmMKOoRTcaxhBzwR9cDPl9sGU3ER/pEl9EEnpnuJyst9kj3kZUW3RuYleYnM81Hj8w0emSl4ffpA1Wkq/L5LFq898xi8uCCk/ZzztEcjHCoJUhDc4hDsUdzMExrOEJLKExrKEJLKHJ0eWQ9HIkQjkDEHdkJceyI5NEdFM5Rkp/Vif9zz51OHtnbtlNH5IuBvbMJhh1m0XtfGNEdPtFl9DkGhmEWnXZ2ZN1iLx7rH33NF3sv2rQd1yf2vn6fEfD7SPdHl2l+H2l+I80fzUXRovJYW0bAR05GgJwMP9npAXLSo7kpPZByV9YSkTMoKc4Scs7NBeZC9BDwB3mPi0f04+IR/To0LhFJTWYW3SGQ7kc3SU4uHZEv7rhseIfGJCLS1SWyi6EGGNjm+YBY2wn7mFkA6En0pLBEflZERLq308kjIiJyhiVSECwFys2szMzSgRnAwnZ9FgKzYuufAhbF5n0uBGaYWYaZlQHlwFsdE7qIiHQRp5NHRETkDDvllKHYXM7bgBeJXi7uUefcajObDVQ65xYCjwC/iZ00vJ/ohz2xfk8QPXEsBHw13hWGRESk+zmdPCIiImee7lQsItL16OoGKF+IiCQgoXyhyxSIiIiIiKQwFQQiIiIiIilMBYGIiIiISApTQSAiIiIiksKS7qRiM9sDbPM6jpg+tLtLpvwDjVF8Gp/4ND7xnWx89jrnpnZ2MMlG+aJL0fjEp/GJT+MTX7zxSShfJF1BkEzMrNI5V+F1HMlMYxSfxic+jU98Gp+uQ7+r+DQ+8Wl84tP4xNcR46MpQyIiIiIiKUwFgYiIiIhIClNBEN9crwPoAjRG8Wl84tP4xKfx6Tr0u4pP4xOfxic+jU98pz0+OodARERERCSF6QiBiIiIiEgKU0EgIiIiIpLCVBC0YWb5ZvaUma0zs7VmNsXMepvZn81sY2zZy+s4vWBmw83s3TaPejO7XeNzjJn9s5mtNrNVZvaYmWWaWZmZvWlmm8zscTNL9zpOr5jZN2Jjs9rMbo+1pez2Y2aPmtluM1vVpu2E42FRc2Lb0Qozm+Bd5ALKF/EoX5ya8kV8yhfH64x8oYLgeP8NvOCcGwGMBdYCdwEvO+fKgZdjz1OOc269c26cc24ccC7QCPwBjQ8AZlYCfB2ocM6NBvzADOCnwD3OuaHAAeAW76L0jpmNBr4ITCT6t3WVmQ0ltbefeUD7m8WcbDwuB8pjj1uBBzopRjk55YuTUL6IT/kiPuWLE5rHGc4XKghizKwncCHwCIBzrtU5dxCYBsyPdZsPXONNhEnlEmCzc24bGp+2AkCWmQWAbKAWuBh4KvZ6Ko/P2cCbzrlG51wIeBWYTgpvP865xcD+ds0nG49pwK9d1BtAvpkVdU6k0p7yxfuifHFiyhcnp3zRTmfkCxUEx5QBe4D/MbNlZvawmeUA/ZxztbE+O4F+nkWYPGYAj8XWNT6Ac64G+DnwHtEP9jrgbeBg7AMNYDtQ4k2EnlsFfNjMCswsG7gCGIi2n/ZONh4lQHWbfqm8LSUD5YvEKV+0o3xxSsoXienQfKGC4JgAMAF4wDk3HjhMu8NRLnqN1pS+TmtsTuPVwJPtX0vl8YnN3ZtG9ItCMZDDPx7eS1nOubVED4e/BLwAvAuE2/VJ2e3nRDQeSU35IgHKFyemfBGf8sX71xHjoYLgmO3Adufcm7HnTxH9wN915FBLbLnbo/iSxeXAO865XbHnGp+oS4Etzrk9zrkg8HvgQ0QP1QVifQYANV4F6DXn3CPOuXOdcxcSnR+7AW0/7Z1sPGqI7iE7IqW3pSSgfJEY5YsTU744BeWLhHRovlBBEOOc2wlUm9nwWNMlwBpgITAr1jYL+D8PwksmMzl2+Bc0Pke8B0w2s2wzM45tP68An4r1SeXxwcwKY8tSovNBf4e2n/ZONh4LgZtjV4+YDNS1OVQsnUz5ImHKFyemfHEKyhcJ6dB8oTsVt2Fm44CHgXSgCvgc0aLpCaAU2AZc55xrf2JHSojNkX0PGOycq4u1FaDxAcDMfgBcD4SAZcAXiM7bWwD0jrXd6Jxr8SxID5nZa0ABEAS+6Zx7OZW3HzN7DLgI6APsAr4HPMMJxiP2peE+otMKGoHPOecqvYhbopQv4lO+iE/5Ij7li+N1Rr5QQSAiIiIiksI0ZUhEREREJIWpIBARERERSWEqCEREREREUpgKAhERERGRFKaCQEREREQkhakgEBERERFJYSoIRERERERS2P8DkBCmPGCPGf8AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 936x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mean = 78.0\n",
"std = 5.2\n",
"neg_inf = mean-4*std\n",
"pos_inf = mean+4*std\n",
"\n",
"# calculate pfobability and cumulative distributions\n",
"x = np.linspace(neg_inf, pos_inf, 1000)\n",
"x_pdf = [norm_pdf(_, mean, std) for _ in x]\n",
"x_cdf = [norm_cdf(_, mean, std) for _ in x]\n",
"\n",
"fig, (ax1, ax2) = get_axes()\n",
"ax1.plot(x, x_pdf)\n",
"ax2.plot(x, x_cdf)\n",
"ax1.set_title('Tomato weight Probability Density Function')\n",
"ax2.set_title('Tomato weight Cumulative Distribution Function')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question a)\n",
"\n",
"> _Assuming that the normal distribution is a reasonable model for the weights of these tomatoes, what proportion of Roma tomatoes are currently undersize (less than 70g) ?_\n",
"\n",
"The tomatoe sizes are normally distributed $\\mathcal{N}(78, 5.2)$. We're looking to estimate the proportion of tomatoes that weigh less than 70g. Mathematically speaking, we're looking for the area under the curve of the normal distribution between -inf and 70. \n",
"\n",
"$$\n",
"P(X<70) = \\int_{-\\infty}^{70} \\mathcal{N}(78, 5.2) \n",
"$$\n",
"\n",
"Or, in terms of the cumulative distribution function, the cumulative probability value for 70. \n"
]
},
{
"cell_type": "code",
"execution_count": 292,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.lines.Line2D at 0x14269ec50>"
]
},
"execution_count": 292,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 936x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_less_than_70 = np.linspace(neg_inf, 70, 200)\n",
"x_pdf_less_than_70 = [norm(_, mean, std) for _ in x_lt_70]\n",
"\n",
"fig, (ax1, ax2) = get_axes()\n",
"ax1.plot(x, x_pdf)\n",
"ax1.fill_between(x_less_than_70, x_pdf_less_than_70, facecolor='white', hatch='\\\\'*4)\n",
"ax2.plot(x, x_cdf)\n",
"ax2.axvline(x=70, ymin=0, ymax=1, color='black', ls='--', lw=1.3)"
]
},
{
"cell_type": "code",
"execution_count": 293,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Proportion of tomatoes under 70g: 0.061967902836371186\n"
]
}
],
"source": [
"proportion = integrate.quad(lambda x: norm(x, 78, 5.2), -inf, 70)[0]\n",
"print('Proportion of tomatoes under 70g:', proportion)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Answer**: 0.062 i.e. 6.2%"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question b)\n",
"\n",
"> _How much a Roma tomato weigh to be among the heaviest 20% ?_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To weigh among the heaviest 20%, we need to find the weight above which the area under the bell curve is equal to 0.2. In other words, it's the value for which the cumulative probability distribution is be equal to 0.8. \n",
"\n",
"\n",
"$$\n",
"P(X>w) = \\int_{-\\infty}^{w} \\mathcal{N}(78, 5.2) = 0.8\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": 294,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cutoff weight: 82.39319319319318\n"
]
},
{
"data": {
"image/png": 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GARgRG2J0OOTCmBBQm1dVY8HyfacwbYDrXkzc0K3Du6OoogbrDuUZHQoREbmh9Ydz8a/N6bhjVDR+dpnrXltHroEJAbV5aw/lorTKjJuHdTc6FLuNiQ9DZMcALhsiIiKHO1VUiUcX70W/yA545vpEo8OhNoAJAbV5X+zKRmTHAFzeK9ToUOzm7SW4eVgUNh3JR25JldHhEBGRm6ixWPHwZ7tRY7bin3cOQ4AvLyKm5jEhoDYtv7Qam47k48ahUfB2sZ2Jm3Pr8B6wam1CQ0RE5AivrTmCnScK8dLNAxEXFmh0ONRGMCGgNm3Z3lOwWBU3t4GLiRuKCwvEZbGdsXRXFlTV6HCIWpWITBGRVBFJE5G5TfRHi8gGEdktIvtEZJoRcRK1ZdvSC/D2pmOYNbIHZgxpe5+LZBwmBNSmfbErC4O6d0RCl2CjQ7koNw6NQlpeGQ6dLjU6FKJWIyLeAN4EMBVAIoBZItJwYfPTABar6lAAtwP4p3OjJGrbSqtq8NiSvYgOaY+nr+N1A9QyTAiozTqcU4KUUyVtcnagzrQBkfDxEny9l8uGyK2NBJCmqumqagKwEMCMBmMUQAfb/Y4ATjkxPqI274Xlh3CqqBKv3TYYgf4+RodDbQz/YqjN+nJXNny8BDcM7mZ0KBetc6Afrukdjm/2nMJTk/vCq41dB0FkpygA9UtqZQEY1WDMcwBWi8jDAAIBTGzuh5rNZhw5cuSctm7duiEoKAg5OTkoKSk5py86OhoBAQHIyspCRUXFOX09e/aEj48PMjIyYDKZzunr3bs3ACAtLQ1Wq/Wndh8fH/Ts2RNWqxVpaWnnPKddu3bo0aMHqqurceLEiXP6goODERkZifLycmRnn3syoHPnzggPD0dxcTFyc3PP6QsPD0fnzp1RUFCAgoKCc/oiIyMRHByM3NxcFBefuwt6jx490K5dO6ccd0BAAKKjo2EymZCRkXFOX1BQELp164aKigpkZWU57bizs7NRXl5+Tl9cXBx8fX1x4sQJVFdXG3bcnTp1QkREBEpKSpCTk3NOX1hYGEJCQnD27FmcOXOmyePOy8tDUVERfkg7g49XH8AdI3sgMaJ287GWHndCQgJEBMeOHYPF8r89cry9vdGrVy+oKo4ePdrkcdfU1OD48eOtftxdu3ZFhw4dfjru+rp374727dvj1KlTKCsra/K4T548iaqqcwt5XMxx+/v7IyYmpsnjDgwMRFRUFCorK5GZeW4lwbrjLi0txenTp1v9uGNjY+Hn5we7qGqzNwBTAKQCSAMwt4l+fwCLbP3bAMTW6xsEYCuAFAD7AQRc6LWGDx+uRM2xWKx6+Utr9d73txsdyiX7aneWxjy1XLelFxgdCrUddr13u8oNwK0A/lPv8d0AFjQY8yiAx2z3LwdwEIBXEz/rfgDJAJI7duyoqJ1Z+On21Vdfqarq7NmzG/UlJyerqurkyZMb9eXk5Kiqav/+/c9p9/Hx+emX3qFDh3P6YmNjVVW1pKSk0c8bM2aMqqoePHiwUd+sWbNUVXX16tWN+p544glVVX3vvfca9b3xxhuqqjpv3rxGfUuXLlVV1fvuu69R37Zt21RVderUqY36srOzVVV14MCB57R7eXn9dNydO3c+py86OlpVVcvLyxv9vCuuuEJVVVNTUxv13Xbbbaqqunbt2kZ9jz76qKqqfvDBB436XnvtNVVVfeGFFxr1LVmyRFVVH3jggUZ9W7duVVXV66+/vlFfZmamqqoOGTKkUV+d0NDQc9qjoqJUVbWysrLRc0aNGqWqqkePHm3Ud8stt6iq6oYNGxr1PfLII6qq+tFHHzXqe/XVV1VV9eWXX27Ut3DhQlVVfeihhxr1bdmyRVVVp0+f3qgvIyNDVVWHDRvWqM9sNquqakRExDntkZGRqqpqMpkaPeeyyy5TVdX09PRGfTfddJOqqm7evLlR38MPP6yqqp988kmjvvnz56uq6vz58xv1ffLJJ6qq+vDDDzfq27x5s6qq3nTTTY360tPTVVX1sssua9RnMplUVTUyMvKc9oiICFVVNZvNjZ4zbNgwVVXNyMho1Dd9+nRVVd2yZUujvoceekhVVRcuXNio7+WXX1ZV1VdffbVR30cffaSqqo888kijvg0bNqiq6i233NKo7+jRo6p2vk+LNnMxo23t5xEA16L2rM4OALNU9WC9MQ8CGKSqD4jI7QBuUtWfiYgPgF0A7lbVvSISCqBIVc+7PeuIESM0OTn5gjER7TxxFre8tRWv/2wwbhradvYfaEp5tRkjXliLm4dF4cWbBhodDrUNbWoqSUQuB/Ccqk62Pf4DAKjqy/XGpACYoqqZtsfpAEar6nl37xsyZIguXrz4nDbOEHCGoOFxu/sMwWMf/4DNR/Lx9l3D0Ssi6KKPmzMEbjtDYNfnhT0JgT1v5Em2MVttSUAOgHDUXkB2h6reZU8wABMCss9zy1Lw6faT2Pn0RAS3kd2JL+S3n+3G5qP52P7HifDz4aU91Ky2lhD4oPbE0gQA2ag9sXSHqqbUG/MtgEWq+oGI9AOwDkCUXuBDip8X5Ok2pObh3vd34JGJCXhkYm+jwyHXZNfnhT3fPJpa+9nwKs6fxqiqGUAxgFAAvQGoiCSJyC4RebLJSEXuF5FkEUnOz8+3J27yYBarYsX+0xjfJ8ItkgEAmDGkG4oqarAljX//5H5snwtzACQBOITaakIpIjJPRKbbhj0G4D4R2QvgMwC/uFAyQOTpyqvNePrLA4iPCMJvxvYyOhxq41r7omIfAGMAXAagAsA6EdmpquvqD1LVdwC8A9Se8WnlmKiN23a8APml1bh+cKTRoTjMVQnh6NTeF1/vOYXxfbsYHQ6Rw6nqSgArG7Q9U+/+QQBXOjsuorbqtTVHkF1Uic8fuBz+PtyNmC6NPTME2QB61Hvc3dbW5Bjb1HBHAAWonU3YrKpnVLUCtR8Gwy41aPJsy/edRns/b4zvG2F0KA7j5+OFaQMjsTolFxUms9HhEBGRC9ubWYT3vz+Ou0ZHY0RsiNHhkBuwJyHYASBBROJExA+1G8YsazBmGYB7bPdvBbDeNtWbBGCgiLS3JQrXoLZyBNFFqbFYsepADib064L2fu5VNfeGQd1QWWPBhsNcNkRERE0zW6yY+8V+hAf748kpfY0Oh9xEswmBnWs/3wUQKiJpqC0dN9f23EIAr6E2qdgDYJeqrnD8YZCn+OFYAc6Wm3D9IPdZLlRnZFwIwoL8sHL/6eYHExGRR/r4xxM4dLoEz93QHx3c5Do6Mp5dp1jtWPtZBWDmeZ77MYCPLyFGop8s33sKwf4+uKZ3uNGhOJy3l2By/674Ylc2Kk0WtPPjmlAiIvqfM2XV+NuaI7gqIQxTBnQ1OhxyI6xvSG1GtdmCVSk5uLZ/FwT4uueX5WkDI1FZY8HG1POWXiciIg/111WHUWmy4Nkb+kOkTVUfJhfHhIDajO+OnEFplRk3DOpmdCitZlRcCEIC/bDyQE7zg4mIyGPsPlmIxclZmD0mDvERQUaHQ26GCQG1GSv3n0bHdr64Mj7M6FBajY+3Fyb374p1h3JRVXPeDb2JiMiDWK2KZ5elICLYHw9PSDA6HHJDTAioTaixWLH2UC4m9Itw+518pw3sigqTBZuOsNoQEREBi5MzsS+rGH+6rh+C/N2rwh65Bvf+ZkVuY1v6WZRUmTG5v/tfRDW6Zyg6t/dltSEiIkJJVQ3+mpSKkbEhmD7YfZfMkrGYEFCbkJSSgwBfL1yd4H7VhRry9fbCpMSuWHcoj8uGiIg83D83HENhhQnP3JDIC4mp1TAhIJdntSpWH8zBNb3DPaYU57RBkSirNuO7o2eMDoWIiAySVViB974/jpuGRmFAVEejwyE3xoSAXN7erCLkllR7xHKhOlf0CkXHdr74lsuGiIg81qtJqRAAj0/qY3Qo5OaYEJDLS0rJhY+XYELfLkaH4jS1y4a6YM3BXJjMVqPDISIiJ9uXVYSv9pzCr66KQ7dO7YwOh9wcEwJyaaqKpJQcXN4rFB3be9YW7VMHdkVptRk/HOOyISIiT6KqeHHFIYQG+uGBa3oZHQ55ACYE5NKO5pXh+JlyTPKg5UJ1rugVhkA/bySl5BodChEROdHaQ3nYdvwsHrm2N4IDPOtkGBmDCQG5tCTbjr2TEj1nuVCdAF9vjO0TgTUHc2GxqtHhEBGRE9RYrHj520PoFR6I2y/rYXQ45CGYEJBLSzqYg6HRndClQ4DRoRhiUv8uOFNWjT2ZhUaHQkRETvD5ziyk55dj7tR+8PXm1zRyDv6lkcvKKqzAgewSj6ou1NDo6GD4eguXDREReYCqGgveWHsUQ6M7YWK/CKPDIQ/ChIBc1mrbl2BPTghKCnLRt7MXklJyoMplQ0RE7uzjH08gp6QKT0zuw03IyKmYEJDLSkrJQZ8uwYgLCzQ6FMNERUUh+av/4ERBBVJzS40Oh4iIWklZtRlvbTyGMfFhuKJXmNHhkIexKyEQkSkikioiaSIyt4l+fxFZZOvfJiKxtvZYEakUkT2229uODZ/cVUFZNXZknMXk/p53MXF97du3x9t/fghQRdIBLhsiInJX7285joJyEx6fzE3IyPmaTQhExBvAmwCmAkgEMEtEEhsMmw2gUFXjAbwOYH69vmOqOsR2e8BBcZObW3soF1aFR5YbbWjG5HFICPHGyn3ZRodCREStoKjChHc2p2NSYhcM6dHJ6HDIA9kzQzASQJqqpquqCcBCADMajJkB4EPb/c8BTBAufqNLkJSSi6hO7dC/WwejQ3EJt13eB6l55cg8W2F0KERE5GBvb0pHmcmMxyZxdoCMYU9CEAUgs97jLFtbk2NU1QygGECorS9ORHaLyCYRueoS4yUPUFZtxpajZzC5f1ePv6iqoqI2AZhkWzqVlJJjZDhERORgeSVV+OCH45gxuBv6dA02OhzyUK19UfFpANGqOhTAowA+FZFGp3xF5H4RSRaR5Pz8/FYOiVzdxtQ8mCxWj79+AACys7OxceNGxIQGom/X4J8qLxERkXt4c0MazBbFIxN7Gx0KeTB7EoJsAPW3yutua2tyjIj4AOgIoEBVq1W1AABUdSeAYwAa/cWr6juqOkJVR4SHh7f8KMitJKXkIjTQDyNiQ4wOxXBRUVGYOXMmNm7ciEn9u2LHibM4U1ZtdFhEROQAp4sr8dn2TMwc0QOxHlxRj4xnT0KwA0CCiMSJiB+A2wEsazBmGYB7bPdvBbBeVVVEwm0XJUNEegJIAJDumNDJHVWbLdhwOA/XJnaBt5dnLxcCaqsMLVmyBDNnzkRoZSZUgbUHOUtAROQO3tmcDqsqHhzby+hQyMM1mxDYrgmYAyAJwCEAi1U1RUTmich027B3AYSKSBpqlwbVlSa9GsA+EdmD2ouNH1DVs44+CHIfP6QVoKza7NGbkTU0duxYLFmyBI/Pvh3h7bx4HQERkRvIL63GZ9tP4sahUegR0t7ocMjD+dgzSFVXAljZoO2ZeverAMxs4nlLASy9xBjJgySl5CDI3wdXxIc2P9iD1CUFd766FEWmqSirNiPI367/fYmIyAW9u+U4qs1Wzg6QS+BOxeQyLFbFmoO5GNsnHP4+3kaH4xLqqgwBtUnBM7+8ETUWxcbUPAOjIiKiS1FUYcJHWzNw/aBu6BkeZHQ4REwIyHXsPFGIgnITlwvVU1dlqM6vbhyPDn6CpANcNkRE1FZ98EMGyk0WPDSOswPkGpgQkMtISsmBn7cXxvZhpak69asMAYC3l2Da4O5YfzgP1WaLscERtYCITBGRVBFJE5G55xlzm4gcFJEUEfnU2TESOUNpVQ3e/z4D1yZ2Qd+u3HyTXAMTAnIJqoqklByMSQhDcICv0eG4jPpVhuqSgsn9u6LcZMEPxwqMDY7ITrZqc28CmAogEcAsEUlsMCYBwB8AXKmq/QE84vRAiZzg4x9PoriyBnPGxRsdCtFPmBCQSzh4ugRZhZXcjKwJdRcU1yUFV8SHIsjfB6tZbYjajpEA0lQ1XVVNABYCmNFgzH0A3lTVQgBQVV4oQ26n0mTBf75Lx9W9wzG4RyejwyH6CRMCcglJKbnwEmBiPyYETamfFGzd8h3G9gnHmoO5sFjV6NCI7BEFILPe4yxbW7VLDewAACAASURBVH29AfQWke9F5EcRmdLUD+LO9tSWLdxxEgXlJjw8nrMD5FqYEJBLSDqQgxGxIQgN8jc6FJfSsMpQXVLQQ87iTJkJO08UGhgdkUP5oHbzyrEAZgH4t4g0OoXKne2prao2W/CvTekYGReCy2JDjA6H6BxMCMhwGWfKkZpbyupCTWhYZaguKXj1sXvh4wVuUkZtRTaAHvUed7e11ZcFYJmq1qjqcQBHUJsgELmFpTuzkVNSxdkBcklMCMhwdV9qJyVyuVBDDasMAbak4NOPUH1iH5IOnIYqlw2Ry9sBIEFE4kTED8DtAJY1GPMVamcHICJhqF1ClO7MIIlai9lixVub0jC4RyeMiQ8zOhyiRpgQkOGSUnLQv1sHbt3ehKaqDAG1ScGvpoxAVlEVDp4uMS5AIjuoqhnAHABJAA4BWKyqKSIyT0Sm24YlASgQkYMANgB4QlVZSovcwrK9p5B5thIPj4uHiBgdDlEjTAjIUHklVdh1sghTuFzovBpWGarz0E1Xw0tqL8gmcnWqulJVe6tqL1V90db2jKous91XVX1UVRNVdaCqLjQ2YiLHsFgVb25IQ9+uwZjQL8LocIiaxISADLX6YO2X2ckDmBBcSFNJQViQP0bEhCDpwGljgyMiovNadSAHx/LLMWc8ZwfIdTEhIEMlpeQgLiwQCRFBRofiks5XZaguKZjUvwtSc8twoqDcoAiJiOh8VBULNqShZ3ggpg6INDocovNiQkCGKa6owdZjBZjcvyvPmpzH+aoM1SUFdZWZWG2IiMj1rD+ch0OnS/DQ2Hh4e/FzjlwXEwIyzLrDuTBblbsTX8B5qwzZkoJj+7ajf7cOvI6AiMjFqCr+sT4NPULaYfqQbkaHQ3RBTAjIMEkpOejaIQCDu3P79vO5UJWhuvbe7Sux62Qh8kqrjAuUiIjO8X1aAfZkFuGBa3rB15tft8i18S+UDFFhMmPTkXxM7t8FXpxGvaDzVRmqa//kr09CFVhzkLMERESu4h/rj6JLB3/cOry70aEQNcuuhEBEpohIqoikicjcJvr9RWSRrX+biMQ26I8WkTIRedwxYVNbt/lIPqpqrNyd2E4XSgoW/et1eJWf4bIhIiIXsSPjLLYdP4tfX90L/j7eRodD1KxmEwIR8QbwJoCpABIBzBKRxAbDZgMoVNV4AK8DmN+g/zUA3156uOQuklJy0am9L0bGhRgdiktrrsoQAIwbNw6TB0Ti+6P5KK6sMSBKIiKqb8H6NIQG+mHWyGijQyGyiz0zBCMBpKlquqqaACwEMKPBmBkAPrTd/xzABLGVjRGRGwEcB5DimJCprTOZrVh7KBfX9usCH66rvKDmqgzV+dWUy2BRYMPhPOcHSUREP9mXVYRNR/Ix+6o4tPPj7AC1DfZ8G4sCkFnvcZatrckxti3qiwGEikgQgKcAPH/poZK72JpegNIqM5cL2aG5KkN17UN7dEJEsD/LjxIRGWzB+jR0CPDB3aNjjA6FyG6tfXr2OQCvq2rZhQaJyP0ikiwiyfn5+a0cEhktKSUH7f28MSYhzOhQXJ49VYY2btwILy/BtYldsDE1H1U1FuMCJiLyYIdzSrD6YC7uvTIOwQG+RodDZDd7EoJsAD3qPe5ua2tyjIj4AOgIoADAKAB/FZEMAI8A+KOIzGn4Aqr6jqqOUNUR4eHhLT4IajssVsXqlFyM6xuBAF9OpdqjuSpD9Tcpq6yx4LujZ4wLlojIg/1zwzEE+nnj3itjjQ6FqEXsSQh2AEgQkTgR8QNwO4BlDcYsA3CP7f6tANZrratUNVZVYwH8HcBLqrrAQbFTG7TrZCHOlFVzuVAL2ZMUmLIOIDjAh8uGiIgMkJ5fhuX7TuGuy2PQqb2f0eEQtUizCYHtmoA5AJIAHAKwWFVTRGSeiEy3DXsXtdcMpAF4FECj0qREAJB0IAd+3l4Y14czQfawp8pQXfusn92GAZ0V6w7lwmyxGhAtEZHnemvjMfh6e+FXY3oaHQpRi9l1DYGqrlTV3qraS1VftLU9o6rLbPerVHWmqsar6khVTW/iZzynqq86NnxqS1QVq1JyMCYhjGsr7WRvlaG69g0fv4HCihpszzjr/GCJiDxUVmEFvtydjVkjoxEe7G90OEQtxpqP5DQpp0qQVViJyf27GB1Km2FvlaG69g9ffhJiNWM1NykjInKaf21Khwjw62s4O0BtExMCcprVKTnwEmBiPyYE9rK3ylCdyRPHYUhXf3y7/xRU1fkBExF5mNySKixKzsStw7sjsmM7o8MhuihMCMhpVqXkYGRcCEKDOJ3aEvZWGapz5zUDkFtqwv7sYucHS0TkYf69OR0Wq+I318QbHQrRRWNCQE6RlleGI7llrC50kVqSFEzsFwEfL8HK/aw2RETUms6Wm/DJtpOYMbgbokPbGx0O0UVjQkBOsXL/aYgAUwdEGh1Km9KSKkN17Z3a++GK+DCs3H+ay4aIiFrRe1uOo8pswYPjehkdCtElYUJATrFi32lcFhOCrh0DjA6lTWlplaG69usHRuLk2QocyC5xftBERB6guLIGH/6QgWkDIhEfEWx0OESXhAkBtbq0vFKk5pZi2kAuF2qpllYZqmtvX5gGHy/B8v2nnB80EZEH+O8PGSitNnN2gNwCEwJqdSv25dQuFxrI5UIt1dIqQ3Xt9955GxJDvbBiH5cNERE5Wnm1Ge9+fxwT+kagf7eORodDdMmYEFCrW7H/FC6LDUGXDlwudDFaWmWorn3H0n8hq7CS1YaIiBzs020nUVRRg4fGs7IQuQcmBNSqjuaW4khuGa7j7MAluZik4D/P/xaiFqzYd9r5ARMRuamqGgve+S4dY+LDMCy6s9HhEDkEEwJqVSt+qi7E6wcuxsVUGapz3bXjMCjCD8v2ZHPZEBGRgyxOzkR+aTUeGsfZAXIfTAioVa3YdxojY0MQweVCF+ViqwzVuXvsAJwuqcbeLC4bIiK6VCazFW9vPIYRMZ0xumeI0eEQOQwTAmo1R3JLcTSvDNcN4nKhi3WxVYbq2q9N7AJfb8GKfaw2RER0qZbuysKp4io8PCEBImJ0OEQOw4SAWs2KfbXLhaZwudBFu9gqQ3XtHdv54qqEcKzcn8NlQ0REl6DGYsU/N6ZhcPeOuDohzOhwiByKCQG1ClXFiv2nMSouBBHBXC50KS62ylBd+3UDI5FdVIk9mUXOD56IyE18vecUMs9W4uHxnB0g98OEgFrFkdwypOWxupCjXEpSEHD2KPy8vVhtiAwlIlNEJFVE0kRk7gXG3SIiKiIjnBkf0YVYrIp/bkhDYmQHTOgXYXQ4RA7HhIBaxdd7suHtJdyM7BJdSpWhuvZf3HEbEkMEK/afhtXKZUPkfCLiDeBNAFMBJAKYJSKJTYwLBvA7ANucGyHRhS3fdwrpZ8rx8Ph4zg6QW7IrIWjuzI6I+IvIIlv/NhGJtbWPFJE9ttteEbnJseGTK7JaFV/vOYUx8WEIC/I3Opw27VKrDNW1/7h4AU4XV2F7xlnnBU/0PyMBpKlquqqaACwEMKOJcX8BMB9AlTODI7oQq1WxYH0aencJwuT+vCaO3FOzCYGdZ3ZmAyhU1XgAr6P2DR0ADgAYoapDAEwB8C8R8XFU8OSadp4sRHZRJW4c2s3oUNq8S60yVNf+4YuPQSwmfL0n23nBE/1PFIDMeo+zbG0/EZFhAHqo6gpnBkbUnFUpOTiaV4Y54xPg5cXZAXJP9swQ2HNmZwaAD233PwcwQUREVStU1WxrDwDA9Qoe4Kvd2Qjw9cKkRJ5JuVSXWmWozuSJ43B5j/b4Zk82qs0W5x0AkR1ExAvAawAes2Ps/SKSLCLJ+fn5rR8ceTRVxT/Wp6FneCCviSO3Zk9C0OyZnfpjbAlAMYBQABCRUSKSAmA/gAfqJQjkhkxmK1bsP41rE7si0J+TQY5wqVWG6vx6yjCUmazYcJhfosjpsgH0qPe4u62tTjCAAQA2ikgGgNEAljV1YbGqvqOqI1R1RHh4eCuGTASsPZSHQ6dL8NDYeHhzdoDcWKtfVKyq21S1P4DLAPxBRBrVoOQZH/fx3dF8FFXU4MYhXC7kSI5ICq7sFYqwIH98tZvLhsjpdgBIEJE4EfEDcDuAZXWdqlqsqmGqGquqsQB+BDBdVZONCZeobnbgKKJD2mMGP9PIzdmTEDR3ZuecMbZrBDoCKKg/QFUPAShD7VkgNOjjGR838dWeU+jc3hdX9+Z/R0dwRJWhunYfby/cMDgS6w/nobiyxolHQZ7ONjM8B0ASgEMAFqtqiojME5HpxkZH1LRNR/KxL6sYD47tBR9vFmUk92bPX/gFz+zYLANwj+3+rQDWq6ranuMDACISA6AvgAyHRE4up7zajDUHc3DdoEj48s3TIRxVZaiu/aahUTBZrPh2P/ckIOdS1ZWq2ltVe6nqi7a2Z1S14ecJVHUsZwfISKqKN9YdRVSndrh5WHejwyFqdc1+a7PzzM67AEJFJA3AowDqSpOOAbBXRPYA+BLAg6p6xtEHQa5h9cEcVNVYMWNIw0tM6GI5qspQXXvB0d3oGRaIr1htiIjovDam5mP3ySI8NC4efj48wUXuz66/8ubO7KhqlarOVNV4VR2pqum29o9Utb+qDlHVYar6VesdChntq92nENWpHYZHdzY6FLfhqCpDde233XYbBncy4cf0szhVVOm8AyEiaiNUFa+tOYIeIe0wcwRnB8gzMO0lh8gprsJ3R/Nx49BurNPsYI6qMlTX/slLjwAAlu095aQjICJqO9YczMX+7GI8PD6By1/JY/AvnRzii91ZsCpw6/AezQ+mFnNkUrD4vX9C849h6c4sqHJrECKiOlZr7exAXFggbh7K5a/kOZgQ0CVTVXyenIXLYjsjLizQ6HDciiOrDNVvv3dsPxzNK8O+rGInHAURUdvw7YEcHM4pxe8mJLCyEHkU/rXTJdt1shDpZ8oxk7MDDufoKkN1Hp05Fn7egsXJ9fccJCLyXBar4vW1R5AQEYQbBnPfAfIsTAjoki1JzkI7X29MG8Rt3R3N0VWG6to7BPji+kHd8PWebFSaLM45GCIiF/bN3lNIyyvDIxN7c1di8jhMCOiSVJjMWL7vNKYNjESQv4/R4bgdR1cZqt8+c0QPlFVbsCqFexIQkWczW6x4Y91R9O0ajKkDuhodDpHTMSGgS7LqQA7Kqs0szdaKHF1lqK59dM8QxIS2x+IdWc47GCIiF/TF7mwcP1OOR6/tzUp55JGYENAlWZKcheiQ9hgVF2J0KG6tNZKCTZs2Yebw7tiaXoCTBf+7eJmIyJNU1Vjw9zVHMKh7R1yb2MXocIgMwYSALtrJggpsTS/ArcO7Q4RnVFpDa1UZqmvvZsqECLBkJy8uJiLP9NHWEzhVXIW5U/vys4w8FhMCumif7TgJLwGXC7Wi1qoyVNf+67t/hgGh3vh8ZxYsVu5JQESepbiyBgs2pOGa3uG4oleY0eEQGYYJAV0Uk9mKxTsyMaFfF0R2bGd0OG6rtaoM1W/fsegNnC6uwsbUvNY/ICIiF/L2pmMorqzBk1P6GB0KkaGYENBFSUrJQUG5CXeOijY6FLfWmlWG6to/nv8kpKoEH2090foHRETkInKKq/DeluO4cUg39O/W0ehwiAzFhIAuyifbTqB753a4OiHc6FDcXmtVGaozcfw4TO8fik1H8nlxMRF5jDfWHYFVFY9N4uwAERMCarG0vDL8mH4Wd4yKZnk2J2ntpOAPt10NEeCT7ZwlICL3l5ZXhkU7MnHX6Bj0CGlvdDhEhmNCQC326baT8PUWzBzew+hQ3F5rVxmqa+/aMQCT+3fFou2ZqKrhzsVE5N7mrzqM9n4+mDMu3uhQiFwCEwJqkUqTBZ/vzMTk/l0RHuxvdDhur7WrDNVvv3t0DIoqa7ByP3cuJiL39UPaGaw5mIvfjO2F0CB+jhEBTAiohb7cnY2SKjPuGh1jdCgewRlVhuraL+8Vip7hgfjoRy4bIiL3ZLEq5i0/iKhO7TB7TJzR4RC5DLsSAhGZIiKpIpImInOb6PcXkUW2/m0iEmtrv1ZEdorIftu/4x0bPjmTquK974+jf7cO3JnYSZxRZaj+zsV3j47B7pNFOJBd3PoHR0TkZIt2ZOJwTin+OK0fAny9jQ6HyGU0mxCIiDeANwFMBZAIYJaIJDYYNhtAoarGA3gdwHxb+xkAN6jqQAD3APjIUYGT820+egZpeWWYPSaOuzk6UWtfUFy/PaIiA+39vPHe98db/8CIiJyopKoGf1udipGxIZg2sKvR4RC5FHtmCEYCSFPVdFU1AVgIYEaDMTMAfGi7/zmACSIiqrpbVU/Z2lMAtBMRLthro97bchzhwf64blCk0aF4HGclBb+44zZcGSn4Zu8p5JZUtf6BERE5yYL1aThbYcKfr0/kSS2iBuxJCKIAZNZ7nGVra3KMqpoBFAMIbTDmFgC7VLW64QuIyP0ikiwiyfn5+fbGTk6UlleKTUfycffoGPj7cJrVWZxVZah++9d/fQQWq+KDHzJa78CIiJwo40w53v/+OG4d1h0Du3MTMqKGnHJRsYj0R+0yol831a+q76jqCFUdER7Oja5c0XvfZ8DPx4s7EzuZM6sM1bUvfv8tmNK345MfT6C82tx6B0dE5CR/WX4Qft5eeGIyNyEjaoo9CUE2gPoF57vb2pocIyI+ADoCKLA97g7gSwA/V9VjlxowOV9huQlf7MrCTUOiWKLNyZxZZah++/OzrkZJlRmLk+tPDhIRtT2rU3Kw7nAefjshAREdAowOh8gl2ZMQ7ACQICJxIuIH4HYAyxqMWYbai4YB4FYA61VVRaQTgBUA5qrq944Kmpzr/R8yUFVjxa+uYok2Z3NmlaH67bNvnICEzt74z+ZjsFi19Q6QiKgVVZjMeP6bg+jdJQi/ZJlRovNqNiGwXRMwB0ASgEMAFqtqiojME5HptmHvAggVkTQAjwKoK006B0A8gGdEZI/tFuHwo6BWU1ZtxgffH8fk/l2Q0CXY6HA8kjOrDNVvf+y6Icgursa3B7hRGRG1Tf+3Lg3ZRZV44caB8PXm1ktE52PX/x2qulJVe6tqL1V90db2jKous92vUtWZqhqvqiNVNd3W/oKqBqrqkHq3vNY7HHK0T348gZIqMx4cy+3djWREUnBtYhf0Cg/EgvVpsHKWgIjamKO5pfjPd+m4dXh3jOTeOUQXxHSZzquqxoJ/f3ccVyWEYXCPTkaH45GMqDJU1+7tJZgzPh6Hc0qx5lBuKx4lEZFjqSqe/uoAAv198IepfY0Oh8jlMSGg81qyMwtnyqrxm7G9jA7FYxlRZah++w2DuiE2tD3+sf4oVDlLQERtw5KdWdh2/CyenNKHxTCI7MCEgJpUbbbg7Y3HMDS6Ey7v2XBLCXIWo6oM1bVv+W4zHhoXjwPZJdiQytV+ROT6ckuq8JflBzEyNgSzLmOpbCJ7MCGgJi3akYnsokr8fmJv7uhoIKOqDNVv71yShh4h7fDGujTOEtBFE5EpIpIqImkiMreJ/kdF5KCI7BORdSISY0Sc1LapKv705X6YzFbMv3UQvLz4+UVkDyYE1EilyYJ/rE/DyNgQXJUQZnQ4Hs+oKkN17bN+dhsmRlqwN7MIG49wJ3FqORHxBvAmgKkAEgHMEpHEBsN2AxihqoMAfA7gr86NktzBsr2nsPZQHp6Y3AdxYYFGh0PUZjAhoEY++jED+aXVeGwSZwdchdFJwYLH70Z4ey+8siqVFYfoYowEkKaq6apqArAQwIz6A1R1g6rWXUX/I2o3wSSyW35pNZ5dloIhPTrh3iu55wBRSzAhoHOUVZvx1sZjuCohDKN47YDhjKwydE77ooXIXPFPHDxdgm/2nWqFIyU3FwWg/rbXWba285kN4NumOkTkfhFJFpHk/HzOWFEtVcWzyw6gotqCV24dBG8uFSJqESYEdI7/fJeOwooaPDapj9GhEIyvMlS//dP/9yhQmIlXVh1Gtdni+IMlAiAidwEYAeCVpvpV9R1VHaGqI8LDw50bHLmsL3ZlY+X+HPz+2t7cRJPoIjAhoJ/kFFfhX5vSMW1gVwzhvgMuwegqQ/Xbx48bh8evjUdWURU+3XbS8QdL7iwbQI96j7vb2s4hIhMB/AnAdFWtdlJs1MadKCjHM18fwKi4ENx/dU+jwyFqk5gQ0E9eSUqFxaqYO6Wf0aGQjStUGarf/tAtE5AY6o2/r0lFSVWN4w+Y3NUOAAkiEicifgBuB7Cs/gARGQrgX6hNBljjluxitljxyKI98PISvPazIVwqRHSRmBAQAGB/VjGW7srCvWNiER3a3uhwqB6jLyiu3y4i+Osdl6OkyoK/rznaOgdMbkdVzQDmAEgCcAjAYlVNEZF5IjLdNuwVAEEAlojIHhFZdp4fR/STf6xPw+6TRXjppoGI6tTO6HCI2i5Vdanb8OHDlZzLarXqzLd+0GHzVmtJpcnocOg8NmzYoGFhYbphwwbD2//wxT7tOXe5puaUXNpB0cUy/L3aFW78vPBsW4+d0bi5y/X3i3YbHQqRK7Pr/ZQzBIRv9p3G9oyzeHRSbwQH+BodDtXjMlWGGrQ/MakPggJ88dyyFG5WRkROl1dShTmf7kZsWCCen97f6HCI2jwmBB6uuKIG8745iMHdO+J2bvHuclypylD99s6Bfnh8Um/8cKwAK/fnOP7AiYjOo8ZixZxPd6O82oy37xrOE1lEDsCEwMPNTzqMwgoTXrp5IC/GckGuVGWoYfsdo2KQGNkBf1l+kBcYE5HTvJKUiu0ZZ/HyzQPRmyVGiRyCCYEHS844i0+3ncQvr4xF/24djQ6HmuBqVYbqt3+3eRNevnkg8kqr8PLKQ44/eCKiBlbuP413Nqfj55fH4MahF9rbjohaggmBh6qqseAPX+xHVKd2eGRib6PDoQtwhS//52svPLYH913VE59tz8T3aWccf/BERDb7sorw6OI9GBbdCX+6juWxiRzJroRARKaISKqIpInI3Cb6/UVkka1/m4jE2tpDRWSDiJSJyALHhk6X4m+rU3E0rwwv3DQAgf4+RodDzXCFL//nax/un4O4sEDM/WIfKkxmxx88EXm8U0WVmP1hMsKC/PHOz0fA38fb6JCI3EqzCYGIeAN4E8BUAIkAZolIYoNhswEUqmo8gNcBzLe1VwH4M4DHHRYxXbKtxwrwny3HcdfoaIzrE2F0OHQBrlplqH77nbffhtt7WpB5thIvruDSISJyrPJqM371YTIqTRa894vLEBbkb3RIRG7HnhmCkQDSVDVdVU0AFgKY0WDMDAAf2u5/DmCCiIiqlqvqFtQmBuQCSqpq8PiSvYgNDcQfp3HK1dW5apWhhu1P//p2TIn1xSfbTmLVgdOO+wUQkUersVjx8Ge7cTinBAvuGMqLiIlaiT0JQRSAzHqPs2xtTY7R2h0piwGE2huEiNwvIskikpyfn2/v06iFVBVPf3kAOSVVeO22wWjvx6VCrs6Vqww1bF/67M8R19ELT36+D9lFlY77JRCRR7JaFU9+vg/rD+dh3owBGMsZbaJW4xIXFavqO6o6QlVHhIeHGx2O2/rv1hNYtvcUfj8xAUOjOxsdDtnBlasMNWpftBAp/34cJrMFjyzcDbPF6rhfBBF5FFXFvOUH8eXubDw+qTfuGh1jdEhEbs2ehCAbQI96j7vb2pocIyI+ADoCKHBEgOQYO08U4oUVBzGhbwQeHBtvdDjUAi755f887YvfexNFa97CjoxCvPztYcf9EojIY6gqXl9zBB/8kIHZY+Lw0Dh+ZhG1OlW94A2AD4B0AHEA/ADsBdC/wZiHALxtu387gMUN+n8BYEFzr6WqGD58uJJj5ZdW6agX1+qY+eu0qNxkdDh0kTZs2KBhYWG6YcMGl2/vdt1vNeap5bokObNlB0n2ava91BNu/LxwP1arVV9ZdVhjnlquTyzZoxaL1eiQiNo6u95P7RsETANwBMAxAH+ytc0DMN12PwDAEgBpALYD6FnvuRkAzgIoQ+31B4kXei2+wTtWpcmsMxZs0T5Pr9T9WUVGh0MtVF5efs5jV/zy31T72nXrtcfPX9H4P67QnSfO2nGk1EKGfxl3hRs/L9yL1WrVl1Ye1JinlutTn+9lMkDkGI5LCJx54xu841gsVn3go2SNnbtcv91/2uhw6CIcOXLEZb7kt7T9m6T1GjvnAx0+b7VmnClr/mCpJQx/r3aFGz8v3IfFYtVnvz6gMU8t1z99uY/JAJHjMCHwZFarVZ9flqIxTy3Xf28+ZnQ4dJHKy8td6kt+S9s/+Wadxj66WK/8f+s0t7iy+QMmexn+Xu0KN35euIdKk1kf/Hinxjy1XJ9flqJWK5MBIgdiQuDJ6tZgPvv1Ab65tnGu9iW/pe3vfrlWYx//Qie9tpHXsDiO4e/VrnDj50XbV1herbe+9b3GPLVc39l0jJ9XRI7HhMBTvbH2iMY8tVznLuUaTHfhal/yW9q+YMlajX3ya73+/zZrYXl18wdMzTH8vdoVbvy8aNuO5JTouFc2aMIfV+rXe7KNDofIXTEh8DRWq1VfW52qMU8t18cWszqDu3G1L/ktbX9t0RqNfeJrnfz6Js0vrWr+gOlCDH+vdoUbPy/arpX7Tmnin7/V4X9ZrdvSC4wOh8idMSHwJGaLVecu3acxTy3XxxfvUTOTAbfQVqsMna/9H0vWauwTX+q4VzZoVmHFeY6a7GD4e7Ur3Ph50fZU11j0pRW1lYRmLNiip4t4bRFRK2NC4CnKq2v0/v/u0Jinluv8bw9xDaYbactVhs7X/vbStRr72FIdPm81S5JePMPfq13hxs+LtuVobqle93+bNeap5frHL/ZpVY3Z6JCIPAETAk9wPL9MJ7++SWPnLtf3tqQbHQ45WFuvMnS+9o+/Waexcz7UhD+u0K92ZzV98HQhhr9Xu8KNnxdtg9li1Q++P659nl6pQ55P0lUHBN4CdwAADtZJREFUWAabyImYELi7tQdzdOCzq3Tw80m6MTXP6HColbjal3lHtS9LWq89fvHaT2cLK008W9gChr9Xu8KNnxeu70B2kU5fsEVjnlqud7+7jeWHiZyPCYG7Kquq0T98UXu9wNS/b9aTBeXNP4naNFf7Mu+o9jXr1mvk1Ac15qnlOum1TXr4dEnTvwBqyPD3ale48fPCdRWVm3TeNyna8w8rdPhfVuuXu7K4nJXIGEwI3NH3afl61fz1Gjt3ub604iDPqnoQV/sy78j2LoPH6qBnVmj8H1fo35IO8++6eYa/V7vCjZ8XrqfSZNa3N6bpwGdXaezc5Tp36T7uP0JkLCYE7iS7sEIf/KR2J8er5q9nmTYP4W5Vhi7Y3j1OZ72xSmOeWq7jXtmg6w/n8ozi+Rn+Xu0KN35euI6K6v/f3t1HSVXfdxx/f3dmZx+RhQUUEDYoSGw1EvFELU3k1D5oT1ubHi2kJ4n1oZ42scY+nAOm5mhNq2mbHmvTNCdWiKYqNpI2oQs+AGpaUVB8qCJEQJSHlYfd4C67zO7Oztxv/7iX3WXDzi6w7MxwP69z7rlzf/Ob2R/fvdzv/d6nzfojL73vl9+7xhsWNfr1Szf45g/bCj0sEVFBcHpoae/ye1dt9o/f+ZSf91er/J9Wb9XR0xg5HZ8yNFT7t55c41f8/XPesKjRF3z3JX9j10cuP6fg2+pimJQvCu9gR7c/sGarf/KeZ71hUaN/9tsv+rrtzYUeloj0UUFQyva2dvp9q7b4+V97ymcsbvSvLHtd9wrE0On6lKGh2levfc4feel9n/v1cCfji0s2+IvbmnXGoE/Bt9XFMClfFEYQBL5ue7P/6eOv+6yvrvKGRY1+w/de8Q07fqb/oyLFRwVBqQmCwF9+r8W/9Ohrfs4dK/1jixv9tmWv+7b97YUemhRQoXfOC9ne3tXj31q71ed+fbU3LGr0q+5/wR9bv9Nb07G/Jrng2+pimOKcL0ZbEAT+TlObf/OZn/aewbvwrqf9rh9v8nf36WEAIkVMBUEpCILANzW1+r2rNvsv3bfWGxY1+ifufsb/duVm39miMwISKoad80K2d2ay/sQrO33e34RHI2d9daXf+vjrvvqdfZ7ujuUldAXfVhfDFLd8Mdo6M1l/cVuz37tqs8//h+e9YVGjz1jc6Au/+7L/8LXdunxVpDSoIChWbZ0Zf+rtvb74h2/1FgHn3LHSr1+6wZdv3B3XHRwZQrHsnBeyPQgCX/qjNT7lt2/3X/zaSm9Y1Oiz71zlNz38ij+6/gPffqA9LpcsFHxbXQxTHPLFaGrv6vGXtrf4vz6/3b+wZIPPvjMswM+9Y6X/wb+97I+u/8Cb27sKPUwROT7D2p6auzMUM7sKeABIAA+5+zcGvF8BfB+YC/wMWODuH0Tv3QHcBOSA29z9mXw/65JLLvGNGzcOOaZS0dWTY0fzYd7a08qbu8Np6/52AofaiiSXn1vP/NkTufqCyYyvSRV6uFJk0uk01dXVvcsvvPAC1113HU8++STz58+Pd/uChdz17cdoSZ3F6s37aWrtBGBcVZLLZ07gorPrOH/yGZw/+QwmjqkYKtSlxgo9gON1MnlkMKdbvhgt7s6+Q11s29/BtgMdvLvvEP+3u41tB8LcBDBzUi2/PHMCn541gUvPqae2IlnYQYvIiRpWvhiyIDCzBLAV+DVgD/Aq8Dl339yvz5eAT7j7H5vZQuCz7r7AzH4BWAZ8CpgCrAHOc/fcYD+v1Dbw7s6hziwftnWyr62LD9s62XUwzXsHOth+oINdB9O9G9ixVeVcNK2OOdPqmHduPRc3jKM8UVbYf4AUtW3bttHU1FQ8O+FF2n7FFVewo+Uwr75/kP9ev4WXth/Aq8f39p1QW8F5Z9bSUF/NtPHVTI+ms8ZWUl9TQaKs9PavCz2A43EyeSTf95ZavhgtmWxAazrD/kPdNLV28mFr51HzHc2H6ejO9vYfX5PiwqljmTOtjjnT65hzdh3jdIBK5HQxYgXB5cDd7v4b0fIdAO5+X78+z0R9XjazJLAPmAgs7t+3f7/Bft6p2MC7O4FDNggIgnCeC5xs4OQCpycX0NWTozMT0NmTC6dMjs6ebG/boc4eWtMZWjt7+CjdQ1s6w0fpHlo6uklnjq5vUokyPjahmpmTapk5sZZzJ9Vy4dSxzJhQg1lJ5XEpsHQ6TUNDQ1HuhBd9++f/kHseWEL5pBls2dvOe80d7DjQxqHuo7d5ZjC+upz6mhSTzqhifE2KMZVJxlSWM6YySW1FOI2pTFKVSlCRTJBKllGRLOud929LlBkJM8pObZFRUhuSk8kjnidJlWpB4O705JxsENCTdXqCgJ5cQDbnZKJ5Ty6IclNAOpMlncmRzmQ53B3NMznS3Vk6unN8lM5w8HAmnHdkaO+3s39EVXmCKXWVTKmr4twoL82Kpvra0+4Mmoj0GbGC4FrgKne/OVr+AnCpu9/ar8+mqM+eaPk94FLgbmC9uz8atS8BnnL35YP9vBPdwD++YRf3r9ka7ujnjt7hzwZDXxY1HGdUJqmrTjGuupy66hR11eXU11Qwpa6SyWOrmFxXyeSxlUwaU1mKRxylSK1bt44bb7yRpUuXMm/ePLWfZPuan7zIn/zlnXx50V2MnzqDlvZumjsybN35IW++u4OJU2fQQ4L2riyZXDDUryevvuIgfF0GJBNh0TD7rDE8dvNlJ/rVJbWBOZk84u4tg33vieaL2594g7eb2nCg9166I6/xqC3se+SAUm87R97rvxx+PgjCOQPa+3/vSOWk8oRRnQqL1XE15YyrTjG+JsW46hT1NSnG1aSYOKaCqXVVTK2roq66XAekROKpdAoCM7sFuAVg+vTpc3fu3DmcsR9l3fYWVr69l2SZ9SbhRMKi5bK+9jLrfd3/vcpUgqryaEqVUVUeHg2sKk9QWV5GbUWSpC7vEYmV7myOjq4s7dHUlc2RyQZ09877pkw05YKAXAA5997XgYcHJ3ond846o5Lbrpx1okMrqT27kSwIRiJf/OOz77Kj+TBmYGYY4ZmicB4uY2AYZlDW77VFb/b1D98ri76Lfm1H9Ym+N1FmJBNlpBLhvDxRRnnCKE+EuSiVLCNZ1tdWkSyjpiJJTUWC6lSSmlSYm1JJ5SMRGZZh5Yvh3CXUBEzrt3x21HasPnuiU71jCW8KG85ncfcHgQchPOIznIEPNG/mBObNnHAiHxUROaaKZIKK2oQuqTh5J5NHjjIS+eIvfn32iXxMROS0NZxDDK8Cs8xshpmlgIXAigF9VgDXR6+vBZ6LrvtcASw0swozmwHMAl4ZmaGLiEiJOJk8IiIip9iQZwjcPWtmtwLPED4ubqm7v2Nm9wAb3X0FsAT4dzPbDhwk3NgT9fsBsBnIAl/O94QhERE5/ZxMHhERkVNvWH+HYDSV6lMjRERGUUndQ3CqKF+IiAxpWPlCdyWJiIiIiMSYCgIRERERkRhTQSAiIiIiEmMqCEREREREYkwFgYiIiIhIjBXdU4bMrBk4/j89eWpMAFqG7BVvilF+ik9+ik9+g8Wnxd2vGu3BFBvli5Ki+OSn+OSn+OSXLz7DyhdFVxAUEzPb6O6XFHocxUwxyk/xyU/xyU/xKR36XeWn+OSn+OSn+OQ3EvHRJUMiIiIiIjGmgkBEREREJMZUEOT3YKEHUAIUo/wUn/wUn/wUn9Kh31V+ik9+ik9+ik9+Jx0f3UMgIiIiIhJjOkMgIiIiIhJjKgj6MbM6M1tuZj81sy1mdrmZjTez1Wa2LZqPK/Q4C8HMZpvZm/2mQ2Z2u+LTx8z+zMzeMbNNZrbMzCrNbIaZbTCz7Wb2H2aWKvQ4C8XMvhLF5h0zuz1qi+36Y2ZLzeyAmW3q13bMeFjon6P16C0zu7hwIxdQvshH+WJoyhf5KV8cbTTyhQqCoz0APO3uHwcuArYAi4G17j4LWBstx467v+vuc9x9DjAXSAP/heIDgJlNBW4DLnH3C4AEsBD4O+B+d58JfATcVLhRFo6ZXQD8EfApwv9bv2VmM4n3+vMwMPDZ0IPF42pgVjTdAnxnlMYog1O+GITyRX7KF/kpXxzTw5zifKGCIGJmY4HPAEsA3D3j7q3ANcAjUbdHgN8tzAiLypXAe+6+E8WnvyRQZWZJoBrYC/wKsDx6P87xOR/Y4O5pd88CPwF+jxivP+7+P8DBAc2DxeMa4PseWg/Umdnk0RmpDKR8cVyUL45N+WJwyhcDjEa+UEHQZwbQDHzPzN4ws4fMrAY40933Rn32AWcWbITFYyGwLHqt+ADu3gR8E9hFuGFvA14DWqMNGsAeYGphRlhwm4BPm1m9mVUDvwlMQ+vPQIPFYyqwu1+/OK9LxUD5YviULwZQvhiS8sXwjGi+UEHQJwlcDHzH3T8JHGbA6SgPH8kU68cyRdc0/g7w5MD34hyf6Nq9awh3FKYANfz86b3YcvcthKfDnwWeBt4EcgP6xHb9ORbFo6gpXwyD8sWxKV/kp3xx/EYiHioI+uwB9rj7hmh5OeEGf/+RUy3R/ECBxlcsrgZed/f90bLiE/pV4H13b3b3HuA/gXmEp+qSUZ+zgaZCDbDQ3H2Ju891988QXh+7Fa0/Aw0WjybCI2RHxHpdKgLKF8OjfHFsyhdDUL4YlhHNFyoIIu6+D9htZrOjpiuBzcAK4Pqo7XrgxwUYXjH5HH2nf0HxOWIXcJmZVZuZ0bf+PA9cG/WJc3wws0nRfDrh9aCPo/VnoMHisQL4YvT0iMuAtn6nimWUKV8Mm/LFsSlfDEH5YlhGNF/oD5P1Y2ZzgIeAFLADuIGwaPoBMB3YCfy+uw+8sSMWomtkdwHnuHtb1FaP4gOAmf01sADIAm8ANxNet/cEMD5q+7y7dxdskAVkZv8L1AM9wJ+7+9o4rz9mtgyYD0wA9gN3AT/iGPGIdhr+hfCygjRwg7tvLMS4JaR8kZ/yRX7KF/kpXxxtNPKFCgIRERERkRjTJUMiIiIiIjGmgkBEREREJMZUEIiIiIiIxJgKAhERERGRGFNBICIiIiISYyoIRERERERiTAWBiIiIiEiMqSAQEREREYmx/wcLJi2YmKGyrwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 936x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for idx, val in enumerate(x_cdf):\n",
" if val > 0.8:\n",
" break\n",
"weight = x[idx]\n",
"print('Cutoff weight:', weight)\n",
"\n",
"x_greater_than_08 = np.linspace(weight, pos_inf, 200)\n",
"x_pdf_greater_than_08 = [norm(_, mean, std) for _ in x_gt_08]\n",
"\n",
"fig, (ax1, ax2) = get_axes()\n",
"ax1.plot(x, x_pdf)\n",
"ax1.fill_between(x_greater_than_08, x_pdf_greater_than_08, facecolor='white', hatch='\\\\'*4)\n",
"ax2.plot(x, x_cdf)\n",
"ax2.axhline(y=0.8, xmin=0, xmax=100, color='black', ls='--', lw=1.3)\n",
"\n",
"ax1.spines['right'].set_visible(False)\n",
"ax1.spines['top'].set_visible(False)\n",
"ax2.spines['right'].set_visible(False)\n",
"ax2.spines['top'].set_visible(False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Answer**: tomatoes that weigh above 82.4g"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question c)\n",
"\n",
"> _The aim of the current research is to reduce the porportion of undersized tomatoes to no more than 2%. One way of reducing this proportion is to reduce the standard deviation. If the average size of the tomatoes remains 74.0 grams, what must the target standard deviation be to achieve the 2% goal ?_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To find out the standard deviation corresponding to the cutoff of 0.02 at 70 in the cumulative distribution, we can use the standardisation trick. We will work with a normally distributed random variable $Z\\sim\\mathcal{N}(0,1)$ and then convert it back to our random variable $X$ using: \n",
"\n",
"$$\n",
"Z = \\frac{X-\\mu}{\\sigma}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 300,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cutoff Z value: -2.0540540540540544\n",
"Derived Standard deviation: 1.9473684210526312\n"
]
}
],
"source": [
"mean = 0\n",
"std = 1\n",
"neg_inf = mean-4*std\n",
"pos_inf = mean+4*std\n",
"\n",
"z = np.linspace(neg_inf, pos_inf, 1000)\n",
"z_pdf = [norm_pdf(_) for _ in z]\n",
"z_cdf = [norm_cdf(_) for _ in z]\n",
"\n",
"for idx, val in enumerate(z_cdf):\n",
" if val > 0.02:\n",
" break\n",
"z_cutoff = z[idx-1]\n",
"idx_cutoff = idx - 1\n",
"std_answer = (70 - 74)/z_cutoff\n",
"\n",
"print('Cutoff Z value: ', z_cutoff)\n",
"print('Derived Standard deviation:', std_answer)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can verify this by plotting the results"
]
},
{
"cell_type": "code",
"execution_count": 301,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.lines.Line2D at 0x142841f50>"
]
},
"execution_count": 301,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 936x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mean = 74.0\n",
"std = std_answer\n",
"neg_inf = mean-4*std\n",
"pos_inf = mean+4*std\n",
"\n",
"x = np.linspace(neg_inf, pos_inf, 1000)\n",
"x_pdf = [norm_pdf(_, mean, std) for _ in x]\n",
"x_cdf = [norm_cdf(_, mean, std) for _ in x]\n",
"\n",
"x_less_than_002 = np.linspace(neg_inf, 70, 200)\n",
"x_pdf_less_than_002 = [norm(_, mean, std) for _ in x_lt_002]\n",
"\n",
"fig, (ax1, ax2) = get_axes()\n",
"ax1.plot(x, x_pdf)\n",
"ax1.fill_between(x_less_than_002, x_pdf_less_than_002, facecolor='white', hatch='\\\\'*4)\n",
"ax2.plot(x, x_cdf)\n",
"ax2.axhline(y=0.02, xmin=0, xmax=100, color='black', ls='--', lw=1.3)"
]
},
{
"cell_type": "code",
"execution_count": 302,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.019966430368581416"
]
},
"execution_count": 302,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# double check\n",
"proportion = integrate.quad(lambda x: norm(x, 74, 1.947), -inf, 70)[0]\n",
"proportion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Answer:** the results check out. The standard deviation must thus be 1.947 or less"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question d)\n",
"\n",
"> _The company claims that the goal of 2% undersized tomatoes is reached. To test this, a random sample of 20 tomatoes is taken. What is the distribution of the number of undersized tomatoes in this sample if the company's claim is true ? Explain your reasoning._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can think of the tomatoe sampling process as a toss of a (very biased) coin, with a probability of picking an undersized tomatoe being 0.02. That's the definition of a Berouilli trial. We repeat this process 20 more times. The number of undersized tomatoes in the sample become distributed according to a Binomial distribution $\\mathcal{B}(n,p)$ with $n=20$ and $p=0.02$.\n",
"\n",
"The probability of picking $k$ undersized tomatoes after $n$ samples is given by:\n",
"\n",
"$$\n",
"P(X=k) = \\binom{n}{k} p^k (1-p)^{1-k}\n",
"$$\n",
"\n",
"With the binomial coefficient: \n",
"\n",
"$$\n",
" \\binom{n}{k} = \\frac{n!}{k!(n-k)!}\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question e)\n",
"\n",
"> _Suppose there were 3 undersized bomatoes in the random sample of 20. What is the probability of getting at least 3 undersized tomatoes in a random sample of 20 if the company's claim is true. Do you believe the company's claim ? Why or why not ?_"
]
},
{
"cell_type": "code",
"execution_count": 303,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05283028514513447 0.2724930496959568 0.6676079717550945\n",
"Probability: 0.007068693403814219\n"
]
}
],
"source": [
"from scipy.stats import binom\n",
"\n",
"# arguments: k, n, p\n",
"px_2 = binom.pmf(2, 20, 0.02)\n",
"px_1 = binom.pmf(1, 20, 0.02)\n",
"px_0 = binom.pmf(0, 20, 0.02)\n",
"\n",
"print(px_2, px_1, px_0)\n",
"prob = 1 - sum([px_2, px_1, px_0])\n",
"print('Probability:', prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the formula from above the calculation is as follows: \n",
"\n",
"$$\n",
"\\begin{equation}\n",
"\\begin{split}\n",
"P(X\\geqslant3) &= 1 - P(X < 3) \\\\\n",
" &= 1 - \\bigg( P(X=2) + P(X=1) + P(X=0) \\bigg) \\\\\n",
" &= 1 - \\bigg( 0.0528 + 0.2725 + 0.6676 \\bigg) \\\\\n",
" &= 0.0071\n",
"\\end{split}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If their clame is true, the probability of picking 3 undersized tomatoes 🍅 from a sample of 20 is 0.0071 (less than one chance in 140), i.e. less than 1%, which is highly unlikely. \n",
"\n",
"Thus the claim is complete bs, a fail of epic proportions, what else is new in corporate ? 😎 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![meme](https://i.imgflip.com/39jekx.jpg \"is it though ?\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"codemirror_mode": {
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"file_extension": ".py",
"mimetype": "text/x-python",
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"version": "3.7.4"
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"nbformat_minor": 2
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