Copy_of_ContinuousRV9.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/KeivanBolouri/data-science-projects/blob/main/Copy_of_ContinuousRV9.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Continuous Random Variables\n",
        "#Edward Pineda-Castro\n",
        "#Los Angeles City College"
      ],
      "metadata": {
        "id": "6GxcO4C4u4rV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2:** The reaction time x (in minutes) of a certain chemical process follows a uniform probability distribution with 5$\\leq$x$\\leq$10.\n",
        "\n",
        "**(a)** Draw the graph of the density curve.\n",
        "\n"
      ],
      "metadata": {
        "id": "Oo7Mgzvst0WA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Parameters for the uniform distribution\n",
        "min_reaction_time = 5  # Minimum reaction time in minutes\n",
        "max_reaction_time = 10  # Maximum reaction time in minutes\n",
        "\n",
        "# Create a range of reaction times\n",
        "reaction_times = np.linspace(min_reaction_time, max_reaction_time, 1000)\n",
        "\n",
        "# Calculate the probability density function (PDF) for the uniform distribution\n",
        "pdf = np.full_like(reaction_times, 1 / (max_reaction_time - min_reaction_time))\n",
        "\n",
        "# (a) Draw the graph of the density curve\n",
        "plt.plot(reaction_times, pdf, label='PDF')\n",
        "plt.fill_between(reaction_times, pdf, color='green', alpha=0.2, label='Area')\n",
        "plt.title('Uniform Probability Distribution')\n",
        "plt.xlabel('Reaction Time (minutes)')\n",
        "plt.ylabel('Probability Density')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "IuxWEBhdujTI",
        "outputId": "10ca5a9c-186c-43f4-b289-9216fd18eee7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)** What is the probability that the reaction time is between 6 and 8 minutes?"
      ],
      "metadata": {
        "id": "J2mik1kju147"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "probability_between_6_and_8 = (8 - 6) / (max_reaction_time - min_reaction_time)\n",
        "print(f'(b) Probability that reaction time is between 6 and 8 minutes: {probability_between_6_and_8:.2f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GcksTYNnvB1K",
        "outputId": "3e466e1c-9bc5-4ce5-88ae-2e1d4a6efa40"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(b) Probability that reaction time is between 6 and 8 minutes: 0.40\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(c)** What is the probability that the reaction time is less than 8 minutes?"
      ],
      "metadata": {
        "id": "PL_bZncCvXj0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "probability_less_than_8 = (8 - min_reaction_time) / (max_reaction_time - min_reaction_time)\n",
        "print(f'(c) Probability that reaction time is less than 8 minutes: {probability_less_than_8:.2f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pgT6DmYrvcNf",
        "outputId": "9ac92650-9938-45c2-dcce-c418d5c4ef20"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(c) Probability that reaction time is less than 8 minutes: 0.60\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(d)** What is the probability that the reaction time is exactly 7 minutes?"
      ],
      "metadata": {
        "id": "9U6ow1AVvgrS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Parameters for the uniform distribution\n",
        "min_reaction_time = 5  # Minimum reaction time in minutes\n",
        "max_reaction_time = 10  # Maximum reaction time in minutes\n",
        "target_time = 7  # Target time in minutes\n",
        "\n",
        "# Calculate the probability density function (PDF) for the uniform distribution\n",
        "pdf = 1 / (max_reaction_time - min_reaction_time)\n",
        "\n",
        "# Define a small range around the target time (e.g., within 1e-6 of 7 minutes)\n",
        "small_range = 1e-6\n",
        "\n",
        "# (a) Draw the graph of the density curve\n",
        "plt.plot([min_reaction_time, max_reaction_time], [pdf, pdf], label='PDF')\n",
        "plt.fill_between([min_reaction_time, max_reaction_time], [pdf, pdf], color='blue', alpha=0.2, label='Area')\n",
        "plt.title('Uniform Probability Distribution')\n",
        "plt.xlabel('Reaction Time (minutes)')\n",
        "plt.ylabel('Probability Density')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# (d) What is the probability that the reaction time is exactly 7 minutes?\n",
        "probability_exact_7 = pdf * small_range\n",
        "print(f'(d) Probability that reaction time is exactly 7 minutes: {probability_exact_7:.2e}')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "7Mp8FdP-v0-w",
        "outputId": "01cce821-5faa-4f25-e7f9-1e1d6e1b5df7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(d) Probability that reaction time is exactly 7 minutes: 2.00e-07\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(e)** Find the 20th percentile."
      ],
      "metadata": {
        "id": "76KtzEKhwS0L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Parameters for the uniform distribution\n",
        "min_reaction_time = 5  # Minimum reaction time in minutes\n",
        "max_reaction_time = 10  # Maximum reaction time in minutes\n",
        "percentile = 0.2  # 20th percentile\n",
        "\n",
        "# (e) Find the 20th percentile\n",
        "percentile_value =  (max_reaction_time - min_reaction_time) * percentile\n",
        "area = percentile_value + min_reaction_time\n",
        "\n",
        "print(f'(e) 20th percentile: {area:.2f} minutes')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rAAP2U1dwZtC",
        "outputId": "1a2a6f34-218d-43b5-cd2b-45cc45ae047e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6.0\n",
            "(e) 20th percentile: 6.00 minutes\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Application of the Normal Distribution"
      ],
      "metadata": {
        "id": "m7ndIXOtz59n"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 1:** Scores on the Stanford-Binet Intelligence Test are normally distributed with mean μ=10 and standard deviation σ=16 .\n",
        "\n",
        "**(a)** People with IQ scores above 132 are considered to be “gifted”.  What percent of people are gifted?"
      ],
      "metadata": {
        "id": "X_WyMf0FyY0z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# (a) IQ score above 132\n",
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "x = 132\n",
        "\n",
        "prob = 1 - norm.cdf(x, loc = mean, scale=stdv)\n",
        "print(\"Probability of p(X >\",x,\")=\",prob)"
      ],
      "metadata": {
        "id": "oZ0AxkuEyxhu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)** What is the probability that a randomly selected individual has an IQ between 90 and 120?"
      ],
      "metadata": {
        "id": "RBSipxOsy39M"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# (b) IQ score between 90 and 120\n",
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "a = 90\n",
        "b = 120\n",
        "\n",
        "prob = norm.cdf(b, loc = mean, scale=stdv) - norm.cdf(a, loc = mean, scale=stdv)\n",
        "print(\"Probability of p(\",a ,\"< X >\",b,\")=\",prob)"
      ],
      "metadata": {
        "id": "wZfl9Fvzy-ZD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(c)** Find the percentile ranking of an individual whose IQ is 125."
      ],
      "metadata": {
        "id": "xd8h3acIy_nJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# (c) IQ score less than\n",
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "x = 125\n",
        "\n",
        "prob = norm.cdf(x, loc = mean, scale=stdv)\n",
        "print(\"Probability of p( X <\",x,\")=\",prob)"
      ],
      "metadata": {
        "id": "n45rINDbzGir"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Practice 1:**  The reading speed of 6th grades is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.\n",
        "\n",
        "**(a)**  Students who have a reading speed of 90 words per minute or less must take a special reading class.  What percent of 6th grade students must take the special reading class?\n"
      ],
      "metadata": {
        "id": "ExUhFBLwzPeH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Enter your code here:"
      ],
      "metadata": {
        "id": "f1-Z7XP0zmHV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)**  What is the probability that a randomly selected 6th grade student will have a reading speed between 100 and 145?"
      ],
      "metadata": {
        "id": "AiYbhgXSzpZ_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Enter your code here:"
      ],
      "metadata": {
        "id": "42vwvP3Azt2J"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "**(c)** Find the percentile ranking of a student who has a reading speed of 115.\n"
      ],
      "metadata": {
        "id": "Qc2FqMvWzwOP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Enter your code here:"
      ],
      "metadata": {
        "id": "d51G9zJKz0zp"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Finding the value of a Normal Random Variable"
      ],
      "metadata": {
        "id": "gGEGrCNx0HqE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2:** Scores on the Stanford-Binet Intelligence Test are normally distributed with mean μ=100 and standard deviation σ=16.\n",
        "\n",
        "**(a)** Determine the 90th percentile of IQs."
      ],
      "metadata": {
        "id": "jixj1t0g0PUj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# (a) 90th percentiel of IQs\n",
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "\n",
        "x = norm.ppf(.90, loc = mean, scale=stdv)\n",
        "print(\"Value corresponde to CDFx =\", x)"
      ],
      "metadata": {
        "id": "xQNOFc910j49",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0c1ca8b7-9aa1-4ef1-9892-1e461cb2fc0b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Value corresponde to CDFx = 120.5048250487136\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#This is just to verify that you got it right"
      ],
      "metadata": {
        "id": "xeZro2TH1Gul"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "x = 120.50\n",
        "\n",
        "prob = norm.cdf(x, loc = mean, scale=stdv)\n",
        "print(\"Probability of p( X <\",x,\")=\",prob)"
      ],
      "metadata": {
        "id": "vB88Vv2A1MyD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)** Determine the IQs that make up the middle 70% of IQs."
      ],
      "metadata": {
        "id": "gQAZG45r0uWN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# (b) IQs between\n",
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "\n",
        "# just need to change this one\n",
        "prob = .15\n",
        "\n",
        "Left_Area = prob\n",
        "Right_Area = 1 - prob\n",
        "\n",
        "x1 = norm.ppf(Left_Area, loc = mean, scale=stdv)\n",
        "x2 = norm.ppf(Right_Area, loc = mean, scale=stdv)\n",
        "print(\"Value corresponde to CDFx =\", x1, \"and\", x2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OLAYmaJL03mb",
        "outputId": "c5540063-2076-43ab-fa90-8508e40d8175"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Value corresponde to CDFx = 83.41706576809936 and 116.58293423190064\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# To verify that x1 and x2 is in fact 70% in the middle\n",
        "from scipy.stats import norm\n",
        "\n",
        "norm.cdf(116.58,100,16)-norm.cdf(83.42,100,16)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c_t_0F4kEfM8",
        "outputId": "098b6d59-eb7b-4e98-a25b-3edb9b4db03a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6999144741332108"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#This is just to verify that you got it right"
      ],
      "metadata": {
        "id": "qPWNMZAP1DXm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "mean = 100\n",
        "stdv = 16\n",
        "a = 83.42\n",
        "b = 116.58\n",
        "\n",
        "prob = norm.cdf(b, loc = mean, scale=stdv) - norm.cdf(a, loc = mean, scale=stdv)\n",
        "print(\"Probability of p(\",a ,\"< X >\",b,\")=\",prob)"
      ],
      "metadata": {
        "id": "BG7qkzqN1Wkj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Practice 2:**  The reading speed of 6th grades is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.\n",
        "\n",
        "**(a)** What is the reading speed of a 6th grader whose reading speed is at the 95th percentile?\n"
      ],
      "metadata": {
        "id": "sePMMO6S1ZWp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Enter your code here:"
      ],
      "metadata": {
        "id": "_GbHGvYX1s_F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)** A school psychologist wants to determine reading rates for unusual students (both slow and fast).  What are the cutoff points for the unusual readers?"
      ],
      "metadata": {
        "id": "2EXxazrj1wY5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Enter your code here:"
      ],
      "metadata": {
        "id": "5l1Z30e811ah"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#The Central Limit Theorem"
      ],
      "metadata": {
        "id": "TsIJvlL8IEHT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 3:**  In 2000, the mean ACT Math score was 20.7.  If ACT Math scores are normally distributed with a standard deviation of 5, answer the following questions.\n",
        "\n",
        "**(a)** What is the probability that a randomly selected student has an ACT Math score 18 or less?"
      ],
      "metadata": {
        "id": "pIi6Y6vOISOe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "mean = 20.7\n",
        "stdv = 5\n",
        "x = 18\n",
        "\n",
        "prob = norm.cdf(x, loc = mean, scale=stdv)\n",
        "print(\"Probability of p( X <\",x,\")=\",prob)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-oCMdOknIaXl",
        "outputId": "2b0595a6-8702-425b-f73b-6cb9e353d782"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p( X < 18 )= 0.2945985162156981\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "norm.cdf(18,20.7,5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zeK5-GKDKZor",
        "outputId": "eddd7478-086c-458d-b50a-ef9d052b8606"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.2945985162156981"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "norm.cdf(18,20.7,5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WvInFHHA0wqT",
        "outputId": "eab1080f-2ba4-43f5-8258-d3838c426fc2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.2945985162156981"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)**  What is the probability that a random sample of 10 ACT test takers has a mean math score of 18 or less?\n",
        "\n"
      ],
      "metadata": {
        "id": "PiwOgD6eIxpy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "norm.cdf(18,20.7,5/math.sqrt(10))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sZ47zYUh1XyR",
        "outputId": "af245365-e588-4f27-dcaa-51bf665bb6ed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.04385251499101193"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(c)** What is the probability a random sample of size 15 will have a mean math score 3 points within the mean?"
      ],
      "metadata": {
        "id": "E6OQsiVRJKvx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mean = 20.7\n",
        "stdv = 5\n",
        "n = 15\n",
        "a = 20.7-3\n",
        "b = 20.7+3\n",
        "\n",
        "prob = norm.cdf(b, loc = mean, scale=stdv/math.sqrt(n)) - norm.cdf(a, loc = mean, scale=stdv/math.sqrt(n))\n",
        "print(\"Probability of p(\",a ,\"< X >\",b,\")=\",prob)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BpB09XmaJWhX",
        "outputId": "132c3636-bb2d-4a23-c6f7-926c0ba9e0b0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p( 17.7 < X > 23.7 )= 0.9798632484496537\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "norm.cdf(23.7,20.7,5/math.sqrt(15))-norm.cdf(17.7,20.7,5/math.sqrt(15))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hP4qWt6m2VqF",
        "outputId": "df3e2e06-cf63-42ba-b85a-9908d4e77a8f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9798632484496537"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(d)** Find the top 10% of a sample size 10."
      ],
      "metadata": {
        "id": "Ul0gJA-OJr0H"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mean = 20.7\n",
        "stdv = 5\n",
        "n = 10\n",
        "\n",
        "x = norm.ppf(1-.10, loc = mean, scale=stdv/math.sqrt(n))\n",
        "print(\"Value corresponde to CDFx =\", x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_8uNmMDeJymL",
        "outputId": "7a4cc431-45c2-4824-9c94-d412b104cae4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Value corresponde to CDFx = 22.72631094303775\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "norm.ppf(1-.10,20.7,5/math.sqrt(10))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9AZWx5MW3tOH",
        "outputId": "d9930e44-e31d-4b04-fba3-cc01914a3624"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "22.72631094303775"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#To prove that in fact this is the value that is going to be 10%\n",
        "import math\n",
        "1-norm.cdf(22.73,20.7,5/math.sqrt(10))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8iPzcJ_s4JVy",
        "outputId": "23b11d97-67ac-422b-a14b-f31693612b40"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.09959114545279113"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Practice 3:** The quality control manager of a Long John Silver’s restaurant wishes to analyze the length of time that a car spends at the drive thru window waiting for an order.  According to records, it is determine that the mean time spent at the window is 59.3 seconds with a standard deviations of 13.1 seconds.  The distribution of the time at the window is skewed right.\n",
        "\n",
        "**(a)**  To obtain probabilities regarding a sample mean using the normal model, what size sample is required?\n"
      ],
      "metadata": {
        "id": "MDn_zHEGKReh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**n $\\geq$ 30 by CLT**"
      ],
      "metadata": {
        "id": "vuuTOZePKaCb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)**  Suppose we take a random sample of 40 cars.  Describe the sampling distribution of the sample mean."
      ],
      "metadata": {
        "id": "KGhp-Pa1Klst"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**$\\mu$ = $\\mu_\\bar{x}$ = 59.3**\n",
        "\n",
        "**$\\sigma$ = $\\sigma_\\bar{x}$= 13.1/sqrt(40) = 2.07**\n",
        "\n"
      ],
      "metadata": {
        "id": "UNQJbOWBKrMV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(c)** The quality control manager wishes to use a new system.  A random sample of 40 cars results in a sample mean time spent at the window of 56.8 seconds.  What is the probability of obtaining a sample mean of 56.8 seconds or less, assuming that the population mean is 59.3 seconds?"
      ],
      "metadata": {
        "id": "0KeZ_4eCKvKr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "norm.cdf(56.7,59.3,13.1/math.sqrt(40))"
      ],
      "metadata": {
        "id": "P8UZSmIkK2yQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "36f1d5b6-16a6-457b-d23e-3d3b4252fc43"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.10469305647543276"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(d)**: Find the top 10% of a sample size of 35 cars spent at the window?  "
      ],
      "metadata": {
        "id": "SzRRuhihLJYf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "norm.ppf(1-.10,59.3,13.1/math.sqrt(35))"
      ],
      "metadata": {
        "id": "0xxvtesXLPil",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1abbf8a6-eaac-4b9f-c5e4-abf37baf0b5b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "62.137744946677905"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# To verify\n",
        "import math\n",
        "1-norm.cdf(62.14,59.3,13.1/math.sqrt(35))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-EhYSb-L71j1",
        "outputId": "5622f0f1-49b4-4cc2-cdd8-adda89b9bcc8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "102.94999999999999"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Distribution of the Sample Proportion"
      ],
      "metadata": {
        "id": "vsOdouUILcbO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 5:**  According to credicard.com, the proportion of adults who do not own a credit card is 0.29.  Suppose a random sample of 500 adults is asked, “Do you own a credit card?”\n",
        "\n",
        "**(a)** What is the probability that in a random sample of 500 adults, between 25% and 30% do not own a credit card?"
      ],
      "metadata": {
        "id": "IZtXMU83LlF9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mu_phat = 0.29\n",
        "n = 500\n",
        "stdv = math.sqrt(mu_phat*(1-mu_phat)/n)\n",
        "a = 0.25\n",
        "b = 0.30\n",
        "\n",
        "prob = norm.cdf(b, loc = mu_phat, scale=stdv) - norm.cdf(a, loc = mu_phat, scale=stdv)\n",
        "print(\"Probability of p(\",a ,\"< p_hat >\",b,\")=\",prob)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_Q9SEW4zLv3s",
        "outputId": "640ee829-7690-400f-c428-2ceea2d79def"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p( 0.25 < p_hat > 0.3 )= 0.6645633825828448\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "norm.cdf(.30, .29, math.sqrt(.29*(1-.29)/500)) - norm.cdf(.25, .29, math.sqrt(.29*(1-.29)/500))\n",
        "125/500"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RiP8liiUSED5",
        "outputId": "30b24c99-de10-410c-f83d-d5afe28312de"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.25"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)**  Would it be unusual for a random sample of 500 adults to result in 125 or fewer who do not own a credit card?  Why?"
      ],
      "metadata": {
        "id": "UrItWD8mNItn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mu_phat = 0.29\n",
        "x = 125\n",
        "n = 500\n",
        "stdv = math.sqrt(mu_phat*(1-mu_phat)/n)\n",
        "phat = x/n\n",
        "\n",
        "prob = norm.cdf(phat, loc = mu_phat, scale=stdv)\n",
        "print(\"Probability of p( p_hat <\",phat,\")=\",prob)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qlYzUBWzNWqM",
        "outputId": "dbe65761-b539-4a9b-d704-bb0c647aa8f5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p( p_hat < 0.25 )= 0.02435410118670095\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "norm.cdf(.25, .29, math.sqrt(.29*(1-.29)/500))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zJksrJ5pS7sM",
        "outputId": "fea1aa12-9539-4d29-c59b-373480f4af66"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.02435410118670095"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Practice 4:** The Pew Research Center recently reported that 18% of women 40-44 years old have never given birth.  Suppose a random sample of 250 adult women aged 40-44 years old is taken.\n",
        "\n",
        "**(a)** What is the probability that in a random sample of 250 women aged 40-44 years less than 10% have never given birth?\n"
      ],
      "metadata": {
        "id": "a-g3CpEQNVqM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mu_phat = 0.18\n",
        "n = 250\n",
        "stdv = math.sqrt(mu_phat*(1-mu_phat)/n)\n",
        "a = 0.10\n",
        "\n",
        "\n",
        "prob = norm.cdf(a, loc = mu_phat, scale=stdv)\n",
        "print(\"Probability of p\",prob)"
      ],
      "metadata": {
        "id": "vnAziB5dOyyY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e6367706-79fd-4a98-8f87-8bba3ad0c1cc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p 0.0004966245888805816\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "norm.cdf(.10, .18, math.sqrt(.18*(1-.18)/250))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BCB09B2eTnxQ",
        "outputId": "8f1aaf4d-a0bc-49c0-be1d-668cb01ff209"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0004966245888805816"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(b)**  What is the probability that in a random sample of 250 women aged 40-44 years old between 15% and 22% have never given birth?"
      ],
      "metadata": {
        "id": "htjMNDFlO1wC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mu_phat = 0.18\n",
        "n = 250\n",
        "stdv = math.sqrt(mu_phat*(1-mu_phat)/n)\n",
        "a = 0.15\n",
        "b = 0.22\n",
        "\n",
        "prob = norm.cdf(b, loc = mu_phat, scale=stdv) - norm.cdf(a, loc = mu_phat, scale=stdv)\n",
        "print(\"Probability of p(\",a ,\"< p_hat >\",b,\")=\",prob)"
      ],
      "metadata": {
        "id": "f9Ks4-IOO6p7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ba9f04c-5d4e-4899-a913-3780a5f878ac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p( 0.15 < p_hat > 0.22 )= 0.8416621885316495\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "norm.cdf(.22, .18, math.sqrt(.18*(1-.18)/250))-norm.cdf(.15, .18, math.sqrt(.18*(1-.18)/250))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PhtYjtrkUPY3",
        "outputId": "9f5ddb31-4544-41cc-d83b-95c32b0bdb51"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8416621885316495"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**(c)** Would it be unusual that in a random sample of 250 women aged 40-44 years old that 35 or more of them have never given birth?"
      ],
      "metadata": {
        "id": "i-aKuNTnO9tE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "import math\n",
        "mu_phat = 0.18\n",
        "x = 35\n",
        "n = 250\n",
        "stdv = math.sqrt(mu_phat*(1-mu_phat)/n)\n",
        "phat = x/n\n",
        "\n",
        "prob = 1- norm.cdf(phat, loc = mu_phat, scale=stdv)\n",
        "print(\"Probability of p=\",prob)"
      ],
      "metadata": {
        "id": "FpjKaeM4PCrI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "845582cb-aadf-4f95-f8cc-8e3df274661f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of p= 0.9501403512824574\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "1-norm.cdf(35/250, .18, math.sqrt(.18*(1-.18)/250))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R5EOQYYXUjQp",
        "outputId": "87f99cf2-2a50-4dd4-ba00-c86d8c1fa742"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9501403512824574"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    }
  ]
}