{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hughes and Hase, Problem 3.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Introduction\n",
    "\n",
    "The probabilities in this problem can be evaluated with the cumulative distribution function, or $C_{DF}$, of a normal distribution.  (This $C_{DF}$ also has the name $\\mbox{Erf}(x)$.) \n",
    "I will use the $C_{DF}$ from the  `stats` sub-module of `scipy`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = 502\n",
    "sigma = 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability that the bag contains less than $500\\, \\mbox{g}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4432015031835318"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(500, mean, sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability is about 44%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability that the bag contains at least  $530\\, \\mbox{g}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02275013194817921"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - stats.norm.cdf(530, mean, sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability is about 2.3%, and so, out of 1000 bags, you would expect about 23 to have a mass greater than 530 g."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Version information\n",
    "`version_information` is from J.R. Johansson (jrjohansson at gmail.com); see <a href='http://nbviewer.jupyter.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-0-Scientific-Computing-with-Python.ipynb'>Introduction to scientific computing with Python</a> for more information and instructions for package installation.\n",
    "\n",
    "`version_information` is installed on the linux network at Bucknell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.7.8 64bit [GCC 7.5.0]"
        },
        {
         "module": "IPython",
         "version": "7.17.0"
        },
        {
         "module": "OS",
         "version": "Linux 3.10.0 1160.36.2.el7.x86_64 x86_64 with centos 7.9.2009 Core"
        },
        {
         "module": "numpy",
         "version": "1.19.1"
        },
        {
         "module": "scipy",
         "version": "1.5.0"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.7.8 64bit [GCC 7.5.0]</td></tr><tr><td>IPython</td><td>7.17.0</td></tr><tr><td>OS</td><td>Linux 3.10.0 1160.36.2.el7.x86_64 x86_64 with centos 7.9.2009 Core</td></tr><tr><td>numpy</td><td>1.19.1</td></tr><tr><td>scipy</td><td>1.5.0</td></tr><tr><td colspan='2'>Fri Feb 04 15:03:33 2022 EST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.7.8 64bit [GCC 7.5.0] \\\\ \\hline\n",
       "IPython & 7.17.0 \\\\ \\hline\n",
       "OS & Linux 3.10.0 1160.36.2.el7.x86\\_64 x86\\_64 with centos 7.9.2009 Core \\\\ \\hline\n",
       "numpy & 1.19.1 \\\\ \\hline\n",
       "scipy & 1.5.0 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Fri Feb 04 15:03:33 2022 EST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.7.8 64bit [GCC 7.5.0]\n",
       "IPython 7.17.0\n",
       "OS Linux 3.10.0 1160.36.2.el7.x86_64 x86_64 with centos 7.9.2009 Core\n",
       "numpy 1.19.1\n",
       "scipy 1.5.0\n",
       "Fri Feb 04 15:03:33 2022 EST"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%version_information numpy, scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
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