Assignment2set2.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOnEQYUuKAqt30XwFHiup5a",
      "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/Rahman17309/ASSIGNMENT1/blob/main/Assignment2set2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 1"
      ],
      "metadata": {
        "id": "JIKW8SUVSmf3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy import stats\n",
        "from scipy.stats import norm"
      ],
      "metadata": {
        "id": "T4ZKYkDWSo-W"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Find Z-Scores at X=50; Z = (X - µ) / σ\n",
        "Z=(50-45)/8\n",
        "Z"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oGvzN0hzSsJV",
        "outputId": "6eb197f6-0677-4806-db7d-91a2c12cb00f"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.625"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Find probability P(X>50) = 1-stats.norm.cdf(abs(z_score))\n",
        "1-stats.norm.cdf(abs(0.625))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z8t_M_fdSsOl",
        "outputId": "16f16a4d-422c-4a72-d1eb-ae039fc1a8f6"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.26598552904870054"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# OR Find probability P(X<=50); p_value=stats.norm.cdf(abs(z_score))\n",
        "p_value=stats.norm.cdf(abs(0.625))\n",
        "p_value"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WXjhSlznSsX9",
        "outputId": "97c8aa81-4a5c-4b0b-823d-b9e6f4a98bff"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7340144709512995"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# P(X>50) = 1 - P(X<=50)\n",
        "1-0.734"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FQ8S1yWZSsg2",
        "outputId": "0f74c67e-b6a6-45a7-9153-ffb1f5f5a9d9"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.266"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 2"
      ],
      "metadata": {
        "id": "VCulf3ufS8C1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# A. More employees at the processing center are older than 44 than between 38 and 44."
      ],
      "metadata": {
        "id": "on3Ph65OS942"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# p(X>44); Employees older than 44 yrs of age\n",
        "1-stats.norm.cdf(44,loc=38,scale=6)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_x6ziWTVS-d3",
        "outputId": "12f13010-e7a9-474e-8ed2-8cd0666fc9d5"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.15865525393145707"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# p(38<X<44); Employees between 38 to 44 yrs of age\n",
        "stats.norm.cdf(44,38,6)-stats.norm.cdf(38,38,6)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G997bXdUS-Wt",
        "outputId": "d8a645b2-627f-4c6f-e7ba-19a43fed67df"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3413447460685429"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# B. A training program for employees under the age of 30 at the center would be expected to attract about 36 employees."
      ],
      "metadata": {
        "id": "ev0LZC1lS-NU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# P(X<30); Employees under 30 yrs of age\n",
        "stats.norm.cdf(30,38,6)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O_oLEjnWTWkB",
        "outputId": "a0af3209-1baa-4ba9-9e38-2a0b18368ad7"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.09121121972586788"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# No. of employees attending training program from 400 nos. is N*P(X<30)\n",
        "400*stats.norm.cdf(30,38,6)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1hNYrMsiTWa8",
        "outputId": "21bd3d8f-45c7-4167-c297-44bf1719ba1a"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "36.484487890347154"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 3"
      ],
      "metadata": {
        "id": "YM4L5F35TdwN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm"
      ],
      "metadata": {
        "id": "DC9u2QkCTgKl"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "mu = 10  # Mean\n",
        "sigma = 2  # Standard Deviation"
      ],
      "metadata": {
        "id": "QgbjwnW9TgpP"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate random samples\n",
        "np.random.seed(0)\n",
        "X1 = np.random.normal(mu, sigma, 1000)\n",
        "X2 = np.random.normal(mu, sigma, 1000)\n"
      ],
      "metadata": {
        "id": "gU3vxVFLTgl1"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate 2X1 and X1 + X2\n",
        "X1_times_2 = 2 * X1\n",
        "X1_plus_X2 = X1 + X2\n"
      ],
      "metadata": {
        "id": "ZBTzk7d9Tgh8"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot histograms\n",
        "plt.figure(figsize=(12, 5))\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.hist(X1_times_2, bins=30, color='blue', alpha=0.7, label='2X1')\n",
        "plt.title('Histogram of 2X1')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Frequency')\n",
        "plt.legend()\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.hist(X1_plus_X2, bins=30, color='green', alpha=0.7, label='X1 + X2')\n",
        "plt.title('Histogram of X1 + X2')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Frequency')\n",
        "plt.legend()\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "id": "EZ05cBmMXh7c",
        "outputId": "93e23bd8-f806-4558-bbe6-b3810c59049e"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 4"
      ],
      "metadata": {
        "id": "WR3-zc-qXzbs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "stats.norm.interval(0.99, loc = 100, scale = 20)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DGJkBSUTX3R2",
        "outputId": "52ee5c93-4e71-446e-818d-639269d044dc"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(48.48341392902199, 151.516586070978)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.round(stats.norm.interval(0.99, loc = 100, scale = 20),1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AtvNd-C9X2sG",
        "outputId": "dbf84ab1-d5d1-49d5-e14d-da0c07f645fe"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 48.5, 151.5])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 5"
      ],
      "metadata": {
        "id": "Cb2RMEOoa2pt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Combine Mean Profit of both division for Company= mean1 + mean2\n",
        "mean1 = 5\n",
        "mean2 = 7\n",
        "Mean = (mean1+mean2) # 1 USD = 45 rupees\n",
        "print('The Mean Profit of both division:',Mean, 'Million$')\n",
        "print('The Mean Profit of both division:',(Mean*45)/10, 'Crore Rupees')\n",
        "\n",
        "# Combine standard Deviation = (Std1^2 + Std2^2)^1/2\n",
        "std1 = 3**2\n",
        "std2 = 4**2\n",
        "Std = np.sqrt(std1 + std2)\n",
        "print('The Standard Deviation of both division:', Std, 'Million$')\n",
        "print('The Standard Deviation of both division:', (Std*45)/10, 'Crore Rupees')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fdZFUiT7mJK-",
        "outputId": "512914ff-7f16-444a-b21c-989ff207bd7f"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The Mean Profit of both division: 12 Million$\n",
            "The Mean Profit of both division: 54.0 Crore Rupees\n",
            "The Standard Deviation of both division: 5.0 Million$\n",
            "The Standard Deviation of both division: 22.5 Crore Rupees\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# A.\tSpecify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company."
      ],
      "metadata": {
        "id": "vvzLxBZRkeyc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "r1, r2 = np.round(stats.norm.interval(0.95, Mean, Std),2)\n",
        "print('Rupee Ranges from',r1,'to',r2,'Million$ in Annual profit of the Company 95% of the time')\n",
        "print('Rupee Ranges from',np.divide(np.multiply(r1,45),10),'to',np.divide(np.multiply(r2,45),10),'Crore Rupees in Annual profit of the Company 95% of the time')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VhB4DNyxkb8U",
        "outputId": "2d89d29d-d5bc-4ec9-f8d2-6556bd722e57"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rupee Ranges from 2.2 to 21.8 Million$ in Annual profit of the Company 95% of the time\n",
            "Rupee Ranges from 9.900000000000002 to 98.1 Crore Rupees in Annual profit of the Company 95% of the time\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# B.\tSpecify the 5th percentile of profit (in Rupees) for the company."
      ],
      "metadata": {
        "id": "1ODk6lvqkkZz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Z value  = X_bar - Mew / Std pop\n",
        "# for percentile, X_percentile = (Zvalue * Std pop) + Mew\n",
        "Z_05_ = stats.norm.ppf(0.05)\n",
        "Fifth_percentile = (Z_05_ * Std) + Mean\n",
        "print('The 5th percentile of Profit for the company is',np.round(Fifth_percentile,2),'Million$')\n",
        "print('The 5th percentile of Profit for the company is',np.round((Fifth_percentile*45)/10,),'Crore Rupees')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OdpT7H5HknaF",
        "outputId": "d4a6dbdc-8e2e-474d-9c54-33b1afa03064"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The 5th percentile of Profit for the company is 3.78 Million$\n",
            "The 5th percentile of Profit for the company is 17.0 Crore Rupees\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#C.\tWhich of the two divisions has a larger probability of making a loss in a given year?"
      ],
      "metadata": {
        "id": "glKyoZw_lvQc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# The probability of Division #1 making a loss\n",
        "print('The Probability of Division #1 making a loss is',np.round((stats.norm.cdf(0,5,3))*100,2),'%')\n",
        "\n",
        "# The probability of Division #2 making a loss\n",
        "print('The Probability of Division #2 making a loss is',np.round((stats.norm.cdf(0,7,4))*100,2),'%')\n",
        "\n",
        "Division_1 = (stats.norm.cdf(0,5,3))*100\n",
        "Division_2 = (stats.norm.cdf(0,7,4))*100\n",
        "\n",
        "if Division_1>Division_2:\n",
        "    print('The Division 1 has a larger Probability of making a loss')\n",
        "else:\n",
        "          print('The Division 2 has a larger Porbability of making a loss')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mwoZTfaFlxkD",
        "outputId": "f46d2297-b920-4810-c9bf-fa46e479deca"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The Probability of Division #1 making a loss is 4.78 %\n",
            "The Probability of Division #2 making a loss is 4.01 %\n",
            "The Division 1 has a larger Probability of making a loss\n"
          ]
        }
      ]
    }
  ]
}