{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_std_normal_with_probability(title, x, interval_1, interval_2=np.array([])):\n",
    "    \"\"\"\n",
    "    Plot the standard normal curve with a filled-in area under\n",
    "    the curve within one or two intervals of the x values.\n",
    "    @param title the title of the graph.\n",
    "    @param x the range of x values to graph.\n",
    "    @param interval_1 one interval of the range.\n",
    "    @param interval_2 another interval of the range (optional).\n",
    "    \"\"\"\n",
    "    mu = 0;\n",
    "    sigma = 1;\n",
    "    y = norm.pdf(x, mu, sigma)\n",
    "    z1 = x[interval_1]\n",
    "    \n",
    "    plt.plot(x, y, color='darkblue')\n",
    "    plt.fill_between(z1, 0, norm.pdf(z1, mu, sigma), color='blue')\n",
    "    \n",
    "    if len(interval_2) > 0:\n",
    "        z2 = x[interval_2]\n",
    "        plt.fill_between(z2, 0, norm.pdf(z2, mu, sigma), color='blue')\n",
    "        \n",
    "    plt.title(title)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-3, 3, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -0.75\n",
    "p = norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z < {z0}) = {p:.4f}', x, x < z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = 0.35\n",
    "p = norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z < {z0}) = {p:.4f}', x, x < z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = 0\n",
    "p = 1 - norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z > {z0}) = {p:.4f}', x, x > z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = 1.645\n",
    "p = 1 - norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z > {z0}) = {p:.4f}', x, x > z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -0.75\n",
    "z1 = 1.50\n",
    "p = norm.cdf(z1) - norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P({z0} < z < {z1}) = {p:.4f}', x, (z0 < x) & (x < z1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -0.81\n",
    "z1 = 1.38\n",
    "p = norm.cdf(z1) - norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P({z0} < z < {z1}) = {p:.4f}', x, (z0 < x) & (x < z1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -0.75\n",
    "z1 = 1.50\n",
    "p = 1 - (norm.cdf(z1) - norm.cdf(z0))\n",
    "plot_std_normal_with_probability(f'P(({z0} < z) or (z > {z1})) = {p:.4f}', x,\n",
    "                                 z0 > x, x > z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -1.645\n",
    "z1 = 1.645\n",
    "p = 1 - (norm.cdf(z1) - norm.cdf(z0))\n",
    "plot_std_normal_with_probability(f'P(({z0} < z) or (z > {z1})) = {p:.4f}', x,\n",
    "                                   z0 > x, x > z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -1.49\n",
    "p = norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z < {z0}) = {p:.4f}', x, x < z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = 2.10\n",
    "p = 1 - norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z > {z0}) = {p:.4f}', x, x > z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z0 = -1.784\n",
    "p = norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z < {z0}) = {p:.4f}', x, x < z0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-4, 4, 0.01)\n",
    "z0 = 3.52\n",
    "p = 1 - norm.cdf(z0)\n",
    "plot_std_normal_with_probability(f'P(z > {z0}) = {p:.4f}', x, x > z0)"
   ]
  }
 ],
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