Basic_Statistics_Level_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "69c8f434",
   "metadata": {},
   "source": [
    "#### Q.7 Calculate Mean, Median, Mode, Variance, Standard Deviation, Range &     comment about the values / draw inferences, for the given dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ad224733",
   "metadata": {},
   "outputs": [],
   "source": [
    "## importing libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50f44f4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Points</th>\n",
       "      <th>Score</th>\n",
       "      <th>Weigh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Unnamed: 0  Points  Score  Weigh\n",
       "0          Mazda RX4    3.90  2.620  16.46\n",
       "1      Mazda RX4 Wag    3.90  2.875  17.02\n",
       "2         Datsun 710    3.85  2.320  18.61\n",
       "3     Hornet 4 Drive    3.08  3.215  19.44\n",
       "4  Hornet Sportabout    3.15  3.440  17.02"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## loading dataset\n",
    "file = pd.read_csv('Q7.csv')\n",
    "file.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "42102505",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Points</th>\n",
       "      <th>Score</th>\n",
       "      <th>Weigh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.596563</td>\n",
       "      <td>3.217250</td>\n",
       "      <td>17.848750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.534679</td>\n",
       "      <td>0.978457</td>\n",
       "      <td>1.786943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.760000</td>\n",
       "      <td>1.513000</td>\n",
       "      <td>14.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.080000</td>\n",
       "      <td>2.581250</td>\n",
       "      <td>16.892500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.695000</td>\n",
       "      <td>3.325000</td>\n",
       "      <td>17.710000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.920000</td>\n",
       "      <td>3.610000</td>\n",
       "      <td>18.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4.930000</td>\n",
       "      <td>5.424000</td>\n",
       "      <td>22.900000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "          Points      Score      Weigh\n",
       "count  32.000000  32.000000  32.000000\n",
       "mean    3.596563   3.217250  17.848750\n",
       "std     0.534679   0.978457   1.786943\n",
       "min     2.760000   1.513000  14.500000\n",
       "25%     3.080000   2.581250  16.892500\n",
       "50%     3.695000   3.325000  17.710000\n",
       "75%     3.920000   3.610000  18.900000\n",
       "max     4.930000   5.424000  22.900000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "86c865b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\AppData\\Local\\Temp/ipykernel_1652/3857692192.py:2: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.\n",
      "  file.mean()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Points     3.596563\n",
       "Score      3.217250\n",
       "Weigh     17.848750\n",
       "dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## mean for Points,Score,Weights\n",
    "file.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ff9b1a65",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\AppData\\Local\\Temp/ipykernel_1652/4208982179.py:2: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.\n",
      "  file.median()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Points     3.695\n",
       "Score      3.325\n",
       "Weigh     17.710\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## median for Points,Score,Weights\n",
    "file.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "26b0656f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.07\n",
       "1    3.92\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## mode for Points\n",
    "file.Points.mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "18eaa76c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.44\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## mode for Score\n",
    "file.Score.mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "eaadd0b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    17.02\n",
       "1    18.90\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## mode for Weights\n",
    "file.Weigh.mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "49dd5888",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\AppData\\Local\\Temp/ipykernel_1652/744068849.py:2: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.\n",
      "  file.var()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Points    0.285881\n",
       "Score     0.957379\n",
       "Weigh     3.193166\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Variance for Points,Score,Weights\n",
    "file.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f4581190",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\AppData\\Local\\Temp/ipykernel_1652/3909208091.py:2: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.\n",
      "  file.std()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Points    0.534679\n",
       "Score     0.978457\n",
       "Weigh     1.786943\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Std for Points,Score,Weights\n",
    "file.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d0b86e06",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Range :- \n",
      "Points : 2.17 \n",
      "Score : 3.9110000000000005 \n",
      "Weights : 8.399999999999999\n"
     ]
    }
   ],
   "source": [
    "## Range for Points,Score,Weights\n",
    "range_points = file.Points.max() - file.Points.min()\n",
    "range_score = file.Score.max() - file.Score.min()\n",
    "range_weights = file.Weigh.max() - file.Weigh.min()\n",
    "print('Range :-','\\nPoints :',range_points,'\\nScore :',range_score,'\\nWeights :',range_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46bc8d2c",
   "metadata": {},
   "source": [
    "The Mean, Median, Mode are showing very close values for all three features Points, Score, Weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3805a71d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Drawing some inferences\n",
    "plt.subplots(figsize=(15,5))\n",
    "plt.subplot(1,3,1)\n",
    "plt.boxplot(file.Points)\n",
    "plt.title('Points')\n",
    "plt.subplot(1,3,2)\n",
    "plt.boxplot(file.Score)\n",
    "plt.title('Score')\n",
    "plt.subplot(1,3,3)\n",
    "plt.boxplot(file.Weigh)\n",
    "plt.title('Weigh')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7c063b3",
   "metadata": {},
   "source": [
    "#### Q9) Calculate Skewness, Kurtosis & draw inferences on the following data Cars speed and distance \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0763a43a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Index</th>\n",
       "      <th>speed</th>\n",
       "      <th>dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Index  speed  dist\n",
       "0      1      4     2\n",
       "1      2      4    10\n",
       "2      3      7     4\n",
       "3      4      7    22\n",
       "4      5      8    16"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## read the file of speed and dist\n",
    "df1 = pd.read_csv('Q9_a.csv')\n",
    "df1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1ebdd5e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Speed :-\n",
      "skewness : -0.11395477012828319 \n",
      "kurtosis : -0.5771474239437371\n",
      "\n",
      "Distance :-\n",
      "skewness : 0.7824835173114966 \n",
      "kurtosis : 0.24801865717051808\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import skew, kurtosis\n",
    "\n",
    "## skewness and kurtosis for speed column\n",
    "speed_skew = skew(df1[\"speed\"])\n",
    "speed_kurt = kurtosis(df1[\"speed\"])\n",
    "print('Speed :-\\n''skewness :',speed_skew,'\\nkurtosis :',speed_kurt)\n",
    "\n",
    "## skewness and kurtosis for dist column\n",
    "dist_skew = skew(df1[\"dist\"])\n",
    "dist_kurt = kurtosis(df1[\"dist\"])\n",
    "print('\\nDistance :-\\n''skewness :',dist_skew,'\\nkurtosis :',dist_kurt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1720996d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0          SP         WT\n",
       "0           1  104.185353  28.762059\n",
       "1           2  105.461264  30.466833\n",
       "2           3  105.461264  30.193597\n",
       "3           4  113.461264  30.632114\n",
       "4           5  104.461264  29.889149"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## read the file of Sp and Weight\n",
    "df2 = pd.read_csv('Q9_b.csv')\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "36f1c8be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ST :-\n",
      "skewness : 1.5814536794423764 \n",
      "kurtosis : 2.7235214865269244\n",
      "\n",
      "WT :-\n",
      "skewness : -0.6033099322115126 \n",
      "kurtosis : 0.8194658792266849\n"
     ]
    }
   ],
   "source": [
    "## skewness and kurtosis for sp column\n",
    "sp_skew = skew(df2[\"SP\"])\n",
    "sp_kurt = kurtosis(df2[\"SP\"])\n",
    "print('ST :-\\n''skewness :',sp_skew,'\\nkurtosis :',sp_kurt)\n",
    "\n",
    "## skewness and kurtosis for wt column\n",
    "wt_skew = skew(df2[\"WT\"])\n",
    "wt_kurt = kurtosis(df2[\"WT\"])\n",
    "print('\\nWT :-\\n''skewness :',wt_skew,'\\nkurtosis :',wt_kurt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ed1a095",
   "metadata": {},
   "source": [
    "#### Q11)  Suppose we want to estimate the average weight of an adult male in    Mexico. We draw a random sample of 2,000 men from a population of 3,000,000 men and weigh them. We find that the average person in our sample weighs 200 pounds, and the standard deviation of the sample is 30 pounds. Calculate 94%,98%,96% confidence interval?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "93c1dd62",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "## Given data\n",
    "pop_size = 3000000\n",
    "sample_size = 2000\n",
    "sample_mean = 200\n",
    "sample_std = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "42d96aac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "94% confidence interval: (198.738325292158, 201.261674707842)\n"
     ]
    }
   ],
   "source": [
    "confi_int_94 = stats.norm.interval(0.94,loc=200,scale=30/np.sqrt(2000))\n",
    "print(\"94% confidence interval:\",confi_int_94)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6edcee21",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "96% confidence interval: (198.62230334813333, 201.37769665186667)\n"
     ]
    }
   ],
   "source": [
    "confi_int_96 = stats.norm.interval(0.96,loc=200,scale=30/np.sqrt(2000))\n",
    "print(\"96% confidence interval:\",confi_int_96)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1454a249",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "98% confidence interval: (198.43943840429978, 201.56056159570022)\n"
     ]
    }
   ],
   "source": [
    "confi_int_98 = stats.norm.interval(0.98,loc=200,scale=30/np.sqrt(2000))\n",
    "print(\"98% confidence interval:\",confi_int_98)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf2e5a0e",
   "metadata": {},
   "source": [
    "#### Q12)  Below are the scores obtained by a student in tests \n",
    "34,36,36,38,38,39,39,40,40,41,41,41,41,42,42,45,49,56\n",
    "1)\tFind mean, median, variance, standard deviation.\n",
    "2)\tWhat can we say about the student marks?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "67628c8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics as stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "04e16768",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([34, 36, 36, 38, 38, 39, 39, 40, 40, 41, 41, 41, 41, 42, 42, 45, 49,\n",
       "       56])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marks = np.array([34,36,36,38,38,39,39,40,40,41,41,41,41,42,42,45,49,56])\n",
    "marks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b411ca80",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean : 41\n"
     ]
    }
   ],
   "source": [
    "print('Mean :',stat.mean(marks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b5fd45b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median : 40.5\n"
     ]
    }
   ],
   "source": [
    "print('Median :',stat.median(marks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "1b396acc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance : 25\n"
     ]
    }
   ],
   "source": [
    "print('Variance :',stat.variance(marks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "de17d440",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard Deviation : 5.0\n"
     ]
    }
   ],
   "source": [
    "print('Standard Deviation :',stat.stdev(marks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3b4ee230",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>students</th>\n",
       "      <th>marks</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>34</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>36</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>36</td>\n",
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       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>38</td>\n",
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       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>38</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>39</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>14</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17</td>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>18</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    students  marks\n",
       "0          1     34\n",
       "1          2     36\n",
       "2          3     36\n",
       "3          4     38\n",
       "4          5     38\n",
       "5          6     39\n",
       "6          7     39\n",
       "7          8     40\n",
       "8          9     40\n",
       "9         10     41\n",
       "10        11     41\n",
       "11        12     41\n",
       "12        13     41\n",
       "13        14     42\n",
       "14        15     42\n",
       "15        16     45\n",
       "16        17     49\n",
       "17        18     56"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marks_df = pd.DataFrame({'students':[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],'marks':(marks)})\n",
    "marks_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b011bda2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        vertical-align: middle;\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>students</th>\n",
       "      <th>marks</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>18.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>9.500000</td>\n",
       "      <td>41.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>5.338539</td>\n",
       "      <td>5.052664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>34.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.250000</td>\n",
       "      <td>38.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>9.500000</td>\n",
       "      <td>40.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>13.750000</td>\n",
       "      <td>41.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>56.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        students      marks\n",
       "count  18.000000  18.000000\n",
       "mean    9.500000  41.000000\n",
       "std     5.338539   5.052664\n",
       "min     1.000000  34.000000\n",
       "25%     5.250000  38.250000\n",
       "50%     9.500000  40.500000\n",
       "75%    13.750000  41.750000\n",
       "max    18.000000  56.000000"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marks_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2725c8ea",
   "metadata": {},
   "source": [
    "we don’t have outliers and the data is slightly skewed towards right because mean is greater than median."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c345ff71",
   "metadata": {},
   "source": [
    "#### Q20) Calculate probability from the given dataset for the below cases\n",
    "*\tP(MPG>38)\n",
    "*\tP(MPG<40)\n",
    "*  P (20<MPG<50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "03286ded",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HP</th>\n",
       "      <th>MPG</th>\n",
       "      <th>VOL</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49</td>\n",
       "      <td>53.700681</td>\n",
       "      <td>89</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>45.696322</td>\n",
       "      <td>92</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>53</td>\n",
       "      <td>50.504232</td>\n",
       "      <td>92</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   HP        MPG  VOL          SP         WT\n",
       "0  49  53.700681   89  104.185353  28.762059\n",
       "1  55  50.013401   92  105.461264  30.466833\n",
       "2  55  50.013401   92  105.461264  30.193597\n",
       "3  70  45.696322   92  113.461264  30.632114\n",
       "4  53  50.504232   92  104.461264  29.889149"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars = pd.read_csv('Cars.csv')\n",
    "cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "883d534d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f8c3af6b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean : 34.422075728024666 \n",
      "Standard Deviation : 9.131444731795982\n"
     ]
    }
   ],
   "source": [
    "## Mean and Stadard Deviation of MPG\n",
    "loc_mpg = cars.MPG.mean()\n",
    "scale_mpg = cars.MPG.std()\n",
    "print('Mean :',loc_mpg,'\\nStandard Deviation :',scale_mpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ed37d89f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(MPG>38) : 0.35\n"
     ]
    }
   ],
   "source": [
    "prob_mpg_greater_than_38 = np.round(1 - stats.norm.cdf(38,loc=loc_mpg,scale=scale_mpg),2)\n",
    "print('P(MPG>38) :',prob_mpg_greater_than_38)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "16b19f2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(MPG<40) : 0.73\n"
     ]
    }
   ],
   "source": [
    "prob_mpg_less_than_40 = np.round(stats.norm.cdf(40,loc=loc_mpg,scale=scale_mpg),2)\n",
    "print('P(MPG<40) :',prob_mpg_less_than_40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "dafd7d94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(20<MPG<50) : 0.02\n"
     ]
    }
   ],
   "source": [
    "prob_mpg_greater_than_20 = np.round(1 - stats.norm.cdf(20,loc=loc_mpg,scale=scale_mpg),2)\n",
    "prob_mpg_less_than_50 = np.round(stats.norm.cdf(50,loc=loc_mpg,scale=scale_mpg),2)\n",
    "prob_mpg_between_20_and_50 = np.round(prob_mpg_less_than_50 - prob_mpg_greater_than_20,2)\n",
    "print('P(20<MPG<50) :',prob_mpg_between_20_and_50)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afea15fe",
   "metadata": {},
   "source": [
    "#### Q 21) Check whether the data follows normal distribution\n",
    "*\tCheck whether the MPG of Cars follows Normal Distribution \n",
    "*\tCheck Whether the Adipose Tissue (AT) and Waist Circumference(Waist)  from wc-at data set  follows Normal Distribution \n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e20d7282",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "79ef7311",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HP</th>\n",
       "      <th>MPG</th>\n",
       "      <th>VOL</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49</td>\n",
       "      <td>53.700681</td>\n",
       "      <td>89</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>45.696322</td>\n",
       "      <td>92</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>53</td>\n",
       "      <td>50.504232</td>\n",
       "      <td>92</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   HP        MPG  VOL          SP         WT\n",
       "0  49  53.700681   89  104.185353  28.762059\n",
       "1  55  50.013401   92  105.461264  30.466833\n",
       "2  55  50.013401   92  105.461264  30.193597\n",
       "3  70  45.696322   92  113.461264  30.632114\n",
       "4  53  50.504232   92  104.461264  29.889149"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars = pd.read_csv('Cars.csv')\n",
    "cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3cb8a320",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(cars['MPG'],bins=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b9711bad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Waist</th>\n",
       "      <th>AT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>74.75</td>\n",
       "      <td>25.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>72.60</td>\n",
       "      <td>25.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>81.80</td>\n",
       "      <td>42.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>83.95</td>\n",
       "      <td>42.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>74.65</td>\n",
       "      <td>29.84</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Waist     AT\n",
       "0  74.75  25.72\n",
       "1  72.60  25.89\n",
       "2  81.80  42.60\n",
       "3  83.95  42.80\n",
       "4  74.65  29.84"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wc_at = pd.read_csv('wc-at.csv')\n",
    "wc_at.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "55b03a9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(wc_at,bins=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c7b14ee",
   "metadata": {},
   "source": [
    "#### Q22) Calculate the Z scores of  90% confidence interval,94% confidence interval, 60% confidence interval "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "1d8cabd9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z scores of 90% confidence interval : -1.6448536269514729\n",
      "Z scores of 94% confidence interval : -1.880793608151251\n",
      "Z scores of 60% confidence interval : -0.8416212335729142\n"
     ]
    }
   ],
   "source": [
    "## Z scores of 90%, 94%, 60% confidence interval\n",
    "print('Z scores of 90% confidence interval :',stats.norm.ppf(0.05))\n",
    "print('Z scores of 94% confidence interval :',stats.norm.ppf(0.03))\n",
    "print('Z scores of 60% confidence interval :',stats.norm.ppf(0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70f67d9e",
   "metadata": {},
   "source": [
    "#### Q23) Calculate the t scores of 95% confidence interval, 96% confidence interval, 99% confidence interval for sample size of 25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7f875b58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t scores of 95% confidence interval : -2.063898561628021\n",
      "t scores of 96% confidence interval : -2.171544676008068\n",
      "t scores of 99% confidence interval : -2.796939504772805\n"
     ]
    }
   ],
   "source": [
    "## t scores of 95%, 96%, 99% confidence interval\n",
    "print('t scores of 95% confidence interval :',stats.t.ppf(0.025,df=24))\n",
    "print('t scores of 96% confidence interval :',stats.t.ppf(0.02,df=24))\n",
    "print('t scores of 99% confidence interval :',stats.t.ppf(0.005,df=24))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b75d566",
   "metadata": {},
   "source": [
    "#### Q24)   A Government  company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The sampled bulbs last an average of 260 days, with a standard deviation of 90 days. If the CEO's claim were true, what is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "61dfd97e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_bar = 260\n",
    "pop_mean = 270\n",
    "sample_std = 90\n",
    "n = 18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8049f665",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.4714045207910317"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_value = (x_bar - pop_mean)/(sample_std/np.sqrt(18))\n",
    "t_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "90ed7df4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of 18 randomly selected bulbs is : 0.32167253567098353\n"
     ]
    }
   ],
   "source": [
    "prob = 1 - stats.t.cdf(abs(t_value),df=17)\n",
    "print('Probability of 18 randomly selected bulbs is :',prob)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}