{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2ac48ee6",
   "metadata": {},
   "source": [
    "# Lesson 13 activity solution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0819d4c1",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "Import the required libraries and load the weather dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ab75cb13",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "891fc841",
   "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>weather_condition</th>\n",
       "      <th>wind_strength</th>\n",
       "      <th>temperature_c</th>\n",
       "      <th>rainfall_inches</th>\n",
       "      <th>humidity_percent</th>\n",
       "      <th>pressure_hpa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.13</td>\n",
       "      <td>48.8</td>\n",
       "      <td>1016.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Snowy</td>\n",
       "      <td>Gale</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.29</td>\n",
       "      <td>89.6</td>\n",
       "      <td>1009.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Rainy</td>\n",
       "      <td>Strong Wind</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1003.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cloudy</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>21.6</td>\n",
       "      <td>0.62</td>\n",
       "      <td>49.3</td>\n",
       "      <td>1006.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Calm</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.09</td>\n",
       "      <td>38.6</td>\n",
       "      <td>1016.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  weather_condition wind_strength  temperature_c  rainfall_inches  \\\n",
       "0             Sunny  Light Breeze            8.2             0.13   \n",
       "1             Snowy          Gale            1.6             0.29   \n",
       "2             Rainy   Strong Wind            7.3             0.01   \n",
       "3            Cloudy  Light Breeze           21.6             0.62   \n",
       "4             Sunny          Calm           12.0             1.09   \n",
       "\n",
       "   humidity_percent  pressure_hpa  \n",
       "0              48.8        1016.5  \n",
       "1              89.6        1009.4  \n",
       "2             100.0        1003.3  \n",
       "3              49.3        1006.9  \n",
       "4              38.6        1016.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the weather dataset\n",
    "url = 'https://media.githubusercontent.com/media/gperdrizet/fullstack-2605/refs/heads/main/data/weather.csv'\n",
    "df = pd.read_csv(url)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d6b885a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.DataFrame'>\n",
      "RangeIndex: 365 entries, 0 to 364\n",
      "Data columns (total 6 columns):\n",
      " #   Column             Non-Null Count  Dtype  \n",
      "---  ------             --------------  -----  \n",
      " 0   weather_condition  365 non-null    str    \n",
      " 1   wind_strength      365 non-null    str    \n",
      " 2   temperature_c      365 non-null    float64\n",
      " 3   rainfall_inches    365 non-null    float64\n",
      " 4   humidity_percent   365 non-null    float64\n",
      " 5   pressure_hpa       365 non-null    float64\n",
      "dtypes: float64(4), str(2)\n",
      "memory usage: 17.2 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ea5fa77a",
   "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>temperature_c</th>\n",
       "      <th>rainfall_inches</th>\n",
       "      <th>humidity_percent</th>\n",
       "      <th>pressure_hpa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>365.000000</td>\n",
       "      <td>365.000000</td>\n",
       "      <td>365.000000</td>\n",
       "      <td>365.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.753425</td>\n",
       "      <td>0.303699</td>\n",
       "      <td>66.182740</td>\n",
       "      <td>1012.346301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.720141</td>\n",
       "      <td>0.311469</td>\n",
       "      <td>18.232318</td>\n",
       "      <td>7.437610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>23.400000</td>\n",
       "      <td>983.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>53.900000</td>\n",
       "      <td>1007.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.700000</td>\n",
       "      <td>0.210000</td>\n",
       "      <td>66.800000</td>\n",
       "      <td>1013.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>10.700000</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>79.400000</td>\n",
       "      <td>1017.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>2.230000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>1039.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       temperature_c  rainfall_inches  humidity_percent  pressure_hpa\n",
       "count     365.000000       365.000000        365.000000    365.000000\n",
       "mean        5.753425         0.303699         66.182740   1012.346301\n",
       "std         7.720141         0.311469         18.232318      7.437610\n",
       "min       -10.000000         0.000000         23.400000    983.700000\n",
       "25%         0.700000         0.080000         53.900000   1007.500000\n",
       "50%         5.700000         0.210000         66.800000   1013.200000\n",
       "75%        10.700000         0.400000         79.400000   1017.600000\n",
       "max        25.000000         2.230000        100.000000   1039.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "080e1009",
   "metadata": {},
   "source": [
    "## Exercise 1: binomial distribution - modeling rainy days\n",
    "\n",
    "**Objective**: Understand and visualize binomial distributions using real weather data.\n",
    "\n",
    "The binomial distribution models the number of successes in a fixed number of independent trials. In weather forecasting, we can use it to model the probability of rainy days over a period of time.\n",
    "\n",
    "**Tasks**:\n",
    "\n",
    "1. **Calculate the probability of rain**:\n",
    "   - Count how many days in the dataset have `rainfall_inches > 0`\n",
    "   - Calculate the proportion of rainy days (this is your probability `p`)\n",
    "   - Print this probability with an interpretation (e.g., \"Based on our data, there's a X% chance of rain on any given day\")\n",
    "\n",
    "2. **Create a theoretical binomial distribution**:\n",
    "   - Assume you're looking at a 30-day period (like a month)\n",
    "   - Using the probability from step 1, calculate the theoretical probability of getting exactly k rainy days for k = 0, 1, 2, ..., 30\n",
    "   - Use `scipy.stats.binom.pmf()`\n",
    "\n",
    "3. **Visualize the distribution**:\n",
    "   - Create a bar plot showing the probability of each possible number of rainy days (0 to 30)\n",
    "   - Add a vertical line showing the expected value (mean = n × p)\n",
    "   - Label the axes appropriately\n",
    "   - Include a title with the probability of rain\n",
    "\n",
    "4. **Interpret** your findings:\n",
    "   - What is the most likely number of rainy days in a 30-day period?\n",
    "   - What is the expected (mean) number of rainy days?\n",
    "   - What's the probability of having 15 or more rainy days in a month?\n",
    "   - How does this distribution help weather forecasters make predictions?\n",
    "   - **Bonus**: Calculate the standard deviation and explain what it tells you about the variability in monthly rainfall patterns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0fa8e75",
   "metadata": {},
   "source": [
    "### Probability of rain calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "996e854d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Based on our data, there's a 19.5% chance of rain on any given day\n"
     ]
    }
   ],
   "source": [
    "rainy_days = len(df[df['weather_condition'] == 'Rainy'])\n",
    "total_days = len(df)\n",
    "p_rain = rainy_days / total_days\n",
    "\n",
    "print(f\"Based on our data, there's a {p_rain*100:.1f}% chance of rain on any given day\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32786f54",
   "metadata": {},
   "source": [
    "### Binomial distribution calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "58ffa8be",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2. Create theoretical binomial distribution\n",
    "n_days = 30\n",
    "k_values = np.arange(0, n_days + 1)\n",
    "probabilities = stats.binom.pmf(k_values, n_days, p_rain)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22f972af",
   "metadata": {},
   "source": [
    "### Binomial distribution plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bc16b9bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3. Visualize the distribution\n",
    "expected_value = n_days * p_rain\n",
    "\n",
    "plt.bar(k_values, probabilities)\n",
    "plt.axvline(expected_value, color='red', linestyle='--', label=f'Expected: {expected_value:.1f}')\n",
    "plt.xlabel('Number of Rainy Days')\n",
    "plt.ylabel('Probability')\n",
    "plt.title(f'Binomial Distribution (n=30, p={p_rain:.3f})')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdb005d0",
   "metadata": {},
   "source": [
    "### Interpretation\n",
    "\n",
    "**Most likely number of rainy days**: The mode of the distribution (tallest bar) shows the most probable outcome - 6 rainy days.\n",
    "\n",
    "**Expected number of rainy days**: The expected value (mean) is `n × p = 5.85`.\n",
    "\n",
    "**Probability of 15+ rainy days**: We can calculate this using the cumulative distribution function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ecbe5a9",
   "metadata": {},
   "source": [
    "### Probability of >= 15 rainy days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5bc3a33e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of 15+ rainy days: 0.0002 (0.02%)\n"
     ]
    }
   ],
   "source": [
    "prob_15_or_more = 1 - stats.binom.cdf(14, n_days, p_rain)\n",
    "\n",
    "print(f\"Probability of 15+ rainy days: {prob_15_or_more:.4f} ({prob_15_or_more*100:.2f}%)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "981ac816",
   "metadata": {},
   "source": [
    "### Extra: Binomial cumulative distribution function (CDF) visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4763a550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CDF plot of the binomial distribution\n",
    "cumulative_probs = stats.binom.cdf(k_values, n_days, p_rain)\n",
    "\n",
    "plt.step(k_values, cumulative_probs, where='post')\n",
    "plt.xlabel('Number of Rainy Days')\n",
    "plt.ylabel('Cumulative Probability')\n",
    "plt.title(f'CDF of Binomial Distribution (n=30, p={p_rain:.3f})')\n",
    "plt.grid(alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c569dd29",
   "metadata": {},
   "source": [
    "**How this helps forecasters**: The binomial distribution allows forecasters to quantify uncertainty in predictions. Instead of just saying \"it might rain,\" they can provide probabilities for different scenarios (e.g., \"there's a 5% chance of more than 15 rainy days this month\")."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "172761bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation: 2.17\n"
     ]
    }
   ],
   "source": [
    "std_dev = np.sqrt(n_days * p_rain * (1 - p_rain))\n",
    "print(f\"Standard deviation: {std_dev:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14e2cba3",
   "metadata": {},
   "source": [
    "**Standard deviation interpretation**: The standard deviation indicates the typical variability in the number of rainy days per month. A higher standard deviation means more unpredictable monthly rainfall patterns."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62e405a7",
   "metadata": {},
   "source": [
    "### Data update `rainfall_inches` vs `weather_condition == \"Rainy\"`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "94e7ca78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rainy_rainfall = df.loc[df['weather_condition'] == 'Rainy', 'rainfall_inches']\n",
    "non_rainy_rainfall = df.loc[df['weather_condition'] != 'Rainy', 'rainfall_inches']\n",
    "\n",
    "plt.boxplot([rainy_rainfall, non_rainy_rainfall], tick_labels=['Rainy', 'Not Rainy'])\n",
    "plt.ylabel('Rainfall (inches)')\n",
    "plt.title('Rainfall by Weather Condition')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b351f396",
   "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>weather_condition</th>\n",
       "      <th>wind_strength</th>\n",
       "      <th>temperature_c</th>\n",
       "      <th>rainfall_inches</th>\n",
       "      <th>humidity_percent</th>\n",
       "      <th>pressure_hpa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.00</td>\n",
       "      <td>48.8</td>\n",
       "      <td>1016.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Snowy</td>\n",
       "      <td>Gale</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.00</td>\n",
       "      <td>89.6</td>\n",
       "      <td>1009.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Rainy</td>\n",
       "      <td>Strong Wind</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1003.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cloudy</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>21.6</td>\n",
       "      <td>0.00</td>\n",
       "      <td>49.3</td>\n",
       "      <td>1006.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Calm</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>38.6</td>\n",
       "      <td>1016.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  weather_condition wind_strength  temperature_c  rainfall_inches  \\\n",
       "0             Sunny  Light Breeze            8.2             0.00   \n",
       "1             Snowy          Gale            1.6             0.00   \n",
       "2             Rainy   Strong Wind            7.3             0.01   \n",
       "3            Cloudy  Light Breeze           21.6             0.00   \n",
       "4             Sunny          Calm           12.0             0.00   \n",
       "\n",
       "   humidity_percent  pressure_hpa  \n",
       "0              48.8        1016.5  \n",
       "1              89.6        1009.4  \n",
       "2             100.0        1003.3  \n",
       "3              49.3        1006.9  \n",
       "4              38.6        1016.0  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_updated = df.copy()\n",
    "df_updated.loc[df_updated['weather_condition'] != 'Rainy', 'rainfall_inches'] = 0\n",
    "df_updated.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cec1874",
   "metadata": {},
   "source": [
    "## Exercise 2: central limit theorem - sampling distribution of rainfall\n",
    "\n",
    "**Objective**: Demonstrate the Central Limit Theorem by creating and analyzing a sampling distribution.\n",
    "\n",
    "The Central Limit Theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution. This is fundamental to statistical inference.\n",
    "\n",
    "**Tasks**:\n",
    "\n",
    "1. **Examine the population distribution**:\n",
    "   - Create a histogram of all `rainfall_inches` values in the dataset\n",
    "   - Calculate and print the population mean and standard deviation\n",
    "   - Note the shape of this distribution (is it normal, skewed, etc.?)\n",
    "\n",
    "2. **Create a sampling distribution**:\n",
    "   - Take 1000 random samples from the rainfall data, each of size n=30\n",
    "   - For each sample, calculate the mean rainfall\n",
    "   - Store all 1000 sample means in a list or array\n",
    "   - Hint: Use `df['rainfall_inches'].sample(n=30, replace=True)` for each sample\n",
    "\n",
    "3. **Visualize the sampling distribution**:\n",
    "   - Create a histogram of the 1000 sample means\n",
    "   - Overlay a normal distribution curve using the theoretical mean (μ) and standard error (σ/√n)\n",
    "   - Add a vertical line at the population mean\n",
    "   - You can use `scipy.stats.norm.pdf()` to create the normal curve\n",
    "   - Label axes and add a descriptive title\n",
    "\n",
    "4. **Compare distributions**:\n",
    "   - Create two side-by-side histograms:\n",
    "     - Left: Original rainfall distribution (from step 1)\n",
    "     - Right: Sampling distribution of means (from step 3)\n",
    "   - Make sure both use the same y-axis scale for comparison\n",
    "   - Include the mean and standard deviation in each subplot title\n",
    "\n",
    "5. **Interpret** your findings:\n",
    "   - How does the shape of the sampling distribution compare to the original distribution?\n",
    "   - Is the sampling distribution approximately normal? (This demonstrates the CLT!)\n",
    "   - Calculate the standard error: population σ divided by √30. How does this compare to the standard deviation of your sample means?\n",
    "   - What does the CLT tell us about why we can use normal-based methods (like confidence intervals) even when our data isn't normally distributed?\n",
    "   - **Bonus**: Repeat the experiment with different sample sizes (n=5, n=10, n=50). How does sample size affect the spread and normality of the sampling distribution?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c879505c",
   "metadata": {},
   "source": [
    "### Population distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "da2ffd4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Population mean: 0.3037\n",
      "Population std: 0.3115\n"
     ]
    }
   ],
   "source": [
    "population_mean = df['rainfall_inches'].mean()\n",
    "population_std = df['rainfall_inches'].std()\n",
    "\n",
    "plt.hist(df['rainfall_inches'], bins=50)\n",
    "plt.xlabel('Rainfall (inches)')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Population Distribution of Rainfall')\n",
    "plt.show()\n",
    "\n",
    "print(f\"Population mean: {population_mean:.4f}\")\n",
    "print(f\"Population std: {population_std:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "305f895b",
   "metadata": {},
   "source": [
    "The population distribution is highly right-skewed with many zero values (no rain) and a long tail of higher rainfall amounts."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2b5ce7c",
   "metadata": {},
   "source": [
    "### Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9b1cacd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "sample_size = 30\n",
    "sample_means = []\n",
    "\n",
    "for _ in range(n_samples):\n",
    "    sample = df['rainfall_inches'].sample(n=sample_size, replace=True)\n",
    "    sample_means.append(sample.mean())\n",
    "\n",
    "sample_means = np.array(sample_means)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af68a64a",
   "metadata": {},
   "source": [
    "### Sampling distribution plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6dd93618",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "standard_error = population_std / np.sqrt(sample_size)\n",
    "\n",
    "# Normal curve\n",
    "x = np.linspace(sample_means.min(), sample_means.max(), 100)\n",
    "\n",
    "plt.title('Sampling Distribution of Sample Means (n=30)')\n",
    "plt.hist(sample_means, bins=30, density=True)\n",
    "plt.plot(x, stats.norm.pdf(x, population_mean, standard_error), label='Normal curve')\n",
    "plt.axvline(population_mean, color='black', label=f'Population mean: {population_mean:.3f}')\n",
    "plt.xlabel('Sample Mean Rainfall (inches)')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebf6dae2",
   "metadata": {},
   "source": [
    "### Sampling distribution versus population comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c0fa2f75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CwrIwMtxNat63devWGUnmwoULdokJqXPmzBkjyWzYsCHFNnzO5X5p/fy8XVBQkJkyZUqS5WPHjjU1atTIxCjtJyPjYYwxN2/eNN7e3mb+/PnGGGMSEhJMQECAeeedd6xtLl68aFxdXc1nn32WucFnkcweE2OM6dmzp2nfvn1mh2oXGR0PY4ypVauWGT16tDGGcyTR7WNiTN47R27evGkaNGhgPv744yTHntPPkcweD2Ny9vlhTOb/7ZqTzhGulLqLuLg4bd26VaGhodZl+fLlU2hoqDZt2pTsNps2bbJpL0lhYWEptkfWSM97J0mXL19WUFCQAgMD1b59e+3du9ce4SID+J3L2WrWrKlixYqpRYsW2rhxo6PDyfOio6Ml3frGOiX8zuVu6f38TI1Dhw6pePHiKl26tLp166YTJ05kNNwslxnjcfXqVd24ccP6e3X06FFFRkba9Onj46P69evniN+jrBiTROvXr5efn58qVKig5557TufOncvU2LNCRsfDGKO1a9fqwIEDaty4sSTOkeTGJFFeOkfGjRsnPz8/9e3bN8m6nHyOZMV4JMqJ54eUNX+75qRzhKLUXfz333+Kj4+Xv7+/zXJ/f/8U5z2JjIxMU3tkjfS8dxUqVNAnn3yir7/+WgsXLlRCQoIaNGigU6dO2SNkpFNKv3MxMTG6du2ag6LCvRQrVkyzZ8/Wl19+qS+//FKBgYFq2rSptm3b5ujQ8qyEhAQNHTpUDz74oKpWrZpiOz7ncrf0fH6mRv369TVv3jytWrVKs2bN0tGjR9WoUSNdunQpoyFnqcwYj5deeknFixe3/mGQuF1O/T3KijGRbt128+mnn2rt2rWaOHGiNmzYoNatWys+Pj5T489s6R2P6OhoeXl5ycXFRW3bttX777+vFi1aSMq758jdxkTKW+fIb7/9prlz5+qjjz5Kdn1OPkeyYjyknHt+SFnzt2tOOkecHR0AkF2EhIQoJCTE+rpBgwaqVKmSPvzwQ73xxhsOjAzIfSpUqKAKFSpYXzdo0EBHjhzRlClTkkxsCvsYMGCA9uzZk2Pm+UHO0rp1a+u/q1evrvr16ysoKEhffPHFXb/1zukmTJigJUuWaP369Tw85f9LaUy6dOli/Xe1atVUvXp1lSlTRuvXr9dDDz3kiFCzlLe3t3bs2KHLly9r7dq1Gj58uEqXLq2mTZs6OjSHudeY5JVz5NKlS+rRo4c++ugjFSlSxNHhOFxqxyOvnB+JctPfrhSl7qJIkSJycnJSVFSUzfKoqKgUJ/IMCAhIU3tkjfS8d3fKnz+/atWqpcOHD2dFiMgkKf3OFShQQO7u7g6KCulRr149CiIOMnDgQH333Xf65ZdfVKJEibu25XMud8uMz8/UKFiwoMqXL5/tP2MzMh7vvvuuJkyYoJ9++knVq1e3Lk/cLioqSsWKFbPps2bNmpkXfBbJijFJTunSpVWkSBEdPnw4W/9Bmd7xyJcvn8qWLSvp1q3s+/fv1/jx49W0adM8e47cbUySk1vPkSNHjujYsWNq166ddVlCQoIkydnZWQcOHMjR50hWjEeZMmWSbJdTzg8pa/52zUnnCLfv3YWLi4vq1KmjtWvXWpclJCRo7dq1NlXJ24WEhNi0l6Q1a9ak2B5ZIz3v3Z3i4+O1e/dum19iZD/8zuUeO3bs4PfNzowxGjhwoFasWKGff/5ZpUqVuuc2/M7lbpnx+Zkaly9f1pEjR7L973x6x2PSpEl64403tGrVKtWtW9dmXalSpRQQEGDTZ0xMjLZs2ZIjfo+yYkySc+rUKZ07dy7XniN3SkhIUGxsrKS8e47c6fYxSU5uPUcqVqyo3bt3a8eOHdafRx55xPqk6cDAwBx9jmTFeCQnp5wfUtb87ZqjzhEHT7Se7S1ZssS4urqaefPmmX379pl+/fqZggULmsjISGOMMT169DAjR460tt+4caNxdnY27777rtm/f78ZO3asyZ8/v9m9e7ejDiHPSut79/rrr5vVq1ebI0eOmK1bt5ouXboYNzc3s3fvXkcdQp506dIls337drN9+3YjyUyePNls377dHD9+3BhjzMiRI02PHj2s7f/55x/j4eFh/ve//5n9+/ebGTNmGCcnJ7Nq1SpHHUKelNb3bcqUKearr74yhw4dMrt37zZDhgwx+fLlMz/99JOjDiFPeu6554yPj49Zv369iYiIsP5cvXrV2obPubwnrZ+fsbGx1t//YsWKmRdeeMFs377dHDp0yNpmxIgRZv369ebo0aNm48aNJjQ01BQpUsScOXPG7seXVmkdjwkTJhgXFxezbNkym9+rS5cu2bQpWLCg+frrr82uXbtM+/btTalSpcy1a9fsfnzpkdljcunSJfPCCy+YTZs2maNHj5qffvrJ1K5d25QrV85cv37dIceYFmkdj7ffftv8+OOP5siRI2bfvn3m3XffNc7Ozuajjz6ytslr58i9xiSvnSN3Su7Jcjn5HMns8cjp54cxWfO3a045RyhKpcL7779vSpYsaVxcXEy9evXM5s2breuaNGlievbsadP+iy++MOXLlzcuLi6mSpUqZuXKlXaOGInS8t4NHTrU2tbf39+0adPGbNu2zQFR523r1q0zkpL8JL5XPXv2NE2aNEmyTc2aNY2Li4spXbq0CQ8Pt3vceV1a37eJEyeaMmXKGDc3N+Pr62uaNm1qfv75Z8cEn4cl955Jsvkd4nMub0rL5+fRo0eTPY9u/51/4oknTLFixYyLi4u57777zBNPPGEOHz5sxyPKmLSMR1BQULLjMXbsWGubhIQE8+qrrxp/f3/j6upqHnroIXPgwAE7HlHGZeaYXL161bRs2dIULVrU5M+f3wQFBZlnnnnG+sdYTpCW8XjllVdM2bJljZubmylUqJAJCQkxS5Yssekvr50j9xqTvHaO3Cm5olROP0cyczxyw/lhTOb/7ZpTzhGLMcZk+eVYAAAAAAAAwG2YUwoAAAAAAAB2R1EKAAAAAAAAdkdRCgAAAAAAAHZHUQoAAAAAAAB2R1EKAAAAAAAAdkdRCgAAAAAAAHZHUQoAAAAAAAB2R1EKAAAAAAAAdkdRCgAAAADuwmKx6KuvvnJ0GDlKesbsq6++UtmyZeXk5KShQ4emapumTZvatA0ODtbUqVPvuk1cXJzKli2r33//XZJ07NgxWSwW7dixI03x3k1q4siI2bNnq127dlnWP2AvFKUAZAt3JhSp8ffff+uBBx6Qm5ubatasmaptXnvtNZu2vXr1UocOHe65XY8ePfT2229bX2d2opHaONJr3759KlGihK5cuZJl+wAAIL3Onj2r5557TiVLlpSrq6sCAgIUFhamjRs3Ojq0TJFY9HByctK///5rsy4iIkLOzs6yWCw6duyYYwK8TXBwsCwWiywWizw8PFStWjV9/PHHae4nIiJCrVu3TtM2/fv316OPPqqTJ0/qjTfeSPM+U2v27NkqVaqUGjRoIEkKDAxURESEqlatmmX7zGx9+vTRtm3b9Ouvvzo6FCBDKEoByJBevXpZE5f8+fOrVKlSevHFF3X9+vU09bN8+fI0Jx9jx46Vp6enDhw4oLVr16Zp27TYuXOnvv/+ew0ePNi67M8//1S/fv2ybJ+ZrXLlynrggQc0efJkR4cCAEASnTt31vbt2zV//nwdPHhQ33zzjZo2bapz5845OrRMdd999+nTTz+1WTZ//nzdd999DoooeePGjVNERIT27Nmj7t2765lnntEPP/yQpj4CAgLk6uqa6vaXL1/WmTNnFBYWpuLFi8vb2zutYaeKMUYffPCB+vbta13m5OSkgIAAOTs7Z8k+s4KLi4uefPJJTZ8+3dGhABlCUQpAhrVq1UoRERH6559/NGXKFH344YcaO3Zsmvrw9fVNc/Jx5MgRNWzYUEFBQSpcuHCatk2L999/X4899pi8vLysy4oWLSoPD48s22dW6N27t2bNmqWbN286OhQAAKwuXryoX3/9VRMnTlSzZs0UFBSkevXqadSoUXrkkUes7SZPnqxq1arJ09NTgYGBev7553X58mXr+nnz5qlgwYL67rvvVKFCBXl4eOjRRx/V1atXNX/+fAUHB6tQoUIaPHiw4uPjrdsFBwfrjTfeUNeuXeXp6an77rtPM2bMuGvMJ0+e1OOPP66CBQvK19dX7du3T9VVTj179lR4eLjNsvDwcPXs2TNJ2z179qh169by8vKSv7+/evToof/++8+6ftWqVWrYsKEKFiyowoUL6+GHH9aRI0es6xOvzlq+fLmaNWsmDw8P1ahRQ5s2bbpnnN7e3goICFDp0qX10ksvydfXV2vWrLGu//PPP9WiRQsVKVJEPj4+atKkibZt22bTx+23790rlvXr11vzwObNm8tisWj9+vU6d+6cunbtqvvuu8961dZnn312z/jvZuvWrTpy5Ijatm2bZKwSb99bv369LBaL1q5dq7p168rDw0MNGjTQgQMHbPr69ttvdf/998vNzU1FihRRx44dbdZfvXpVffr0kbe3t0qWLKk5c+bYrL/XebR+/XrVq1dPnp6eKliwoB588EEdP37cur5du3b65ptvdO3atQyNCeBIFKUAZFjiZfaBgYHq0KGDQkNDbRKX1CQUyc0H8Pbbb6f4QW6xWLR161aNGzdOFotFr732miTppZdeUvny5eXh4aHSpUvr1Vdf1Y0bN9J9bPHx8Vq2bFmSe/bvvH3PYrHo448/VseOHeXh4aFy5crpm2++sdlm7969evjhh1WgQAF5e3urUaNGNsmjJL377rsqVqyYChcurAEDBtjEHhsbqxdeeEH33XefPD09Vb9+fa1fv966/vjx42rXrp0KFSokT09PValSRd9//711fYsWLXT+/Hlt2LAh3eMBAEBm8/LykpeXl7766ivFxsam2C5fvnyaPn269u7dq/nz5+vnn3/Wiy++aNPm6tWrmj59upYsWaJVq1Zp/fr16tixo77//nt9//33WrBggT788EMtW7bMZrt33nlHNWrU0Pbt2zVy5EgNGTLEJpe53Y0bNxQWFiZvb2/9+uuv2rhxo7y8vNSqVSvFxcXd9VgfeeQRXbhwQb/99psk6bffftOFCxeS5BkXL15U8+bNVatWLf31119atWqVoqKi9Pjjj1vbXLlyRcOHD9dff/2ltWvXKl++fOrYsaMSEhJs+nrllVf0wgsvaMeOHSpfvry6du2a6i+oEhIS9OWXX+rChQtycXGxLr906ZJ69uyp3377TZs3b1a5cuXUpk0bXbp06a79pRTL7QWfL7/8UhEREWrQoIGuX7+uOnXqaOXKldqzZ4/69eunHj166I8//khV/Mn59ddfVb58+VR9GfrKK6/ovffe019//SVnZ2f16dPHum7lypXq2LGj2rRpo+3bt2vt2rWqV6+ezfbvvfee6tatq+3bt+v555/Xc889Zz3Oe51HN2/eVIcOHdSkSRPt2rVLmzZtUr9+/WSxWKz9161bVzdv3tSWLVvSPR6AwxkAyICePXua9u3bW1/v3r3bBAQEmPr161uXnTp1yrzzzjtm+/bt5siRI2b69OnGycnJbNmyxdqmSZMmZsiQIdbXQUFBxtfX18yYMcMcOnTIjB8/3uTLl8/8/fffxhhjIiIiTJUqVcyIESNMRESEuXTpkjHGmDfeeMNs3LjRHD161HzzzTfG39/fTJw40drv2LFjTY0aNVKM/07btm0zkkxkZKTN8qCgIDNlyhTra0mmRIkSZvHixebQoUNm8ODBxsvLy5w7d846Br6+vqZTp07mzz//NAcOHDCffPKJ9Xh69uxpChQoYJ599lmzf/9+8+233xoPDw8zZ84c6z6efvpp06BBA/PLL7+Yw4cPm3feece4urqagwcPGmOMadu2rWnRooXZtWuXOXLkiPn222/Nhg0bbOKuX7++GTt2bIrHCwCAIyxbtswUKlTIuLm5mQYNGphRo0aZnTt33nWbpUuXmsKFC1tfh4eHG0nm8OHD1mX9+/c3Hh4e1jzBGGPCwsJM//79ra+DgoJMq1atbPp+4oknTOvWra2vJZkVK1YYY4xZsGCBqVChgklISLCuj42NNe7u7mb16tXJxnr06FEjyWzfvt0MHTrU9O7d2xhjTO/evc2wYcPM9u3bjSRz9OhRY8ytfKZly5Y2fZw8edJIMgcOHEh2H2fPnjWSzO7du232+fHHH1vb7N2710gy+/fvT7aPxPFwcXExnp6extnZ2Ugyvr6+5tChQyluEx8fb7y9vc23335rXXb7mKUmlgsXLhhJZt26dSnux5hb+c6IESOsr5PLIW/P0e40ZMgQ07x5c5tlt78/xhizbt06I8n89NNP1jYrV640ksy1a9eMMcaEhISYbt26pbifoKAg0717d+vrhIQE4+fnZ2bNmmWMufd5dO7cOSPJrF+/PuXBMMYUKlTIzJs3765tgOyMK6UAZNh3330nLy8vubm5qVq1ajpz5oz+97//Wdffd999euGFF1SzZk2VLl1agwYNUqtWrfTFF1/ctd82bdro+eefV9myZfXSSy+pSJEiWrdunSRZ7/v38vJSQECA9da60aNHq0GDBgoODla7du30wgsv3HM/d3P8+HE5OTnJz8/vnm179eqlrl27qmzZsnr77bd1+fJl6zd5M2bMkI+Pj5YsWaK6deuqfPny6t27typUqGDdvlChQvrggw9UsWJFPfzww2rbtq11rqwTJ04oPDxcS5cuVaNGjVSmTBm98MILatiwofU2gBMnTujBBx9UtWrVVLp0aT388MNq3LixTYzFixe3uewbAIDsoHPnzjp9+rS++eYbtWrVSuvXr1ft2rU1b948a5uffvpJDz30kO677z55e3urR48eOnfunK5evWpt4+HhoTJlylhf+/v7Kzg42OYWfH9/f505c8Zm/yEhIUle79+/P9lYd+7cqcOHD8vb29t6lZevr6+uX7+e5Aro5PTp00dLly5VZGSkli5danP1ze37WLdunbV/Ly8vVaxYUZKs+zh06JC6du2q0qVLq0CBAgoODpZ0Kx+4XfXq1a3/LlasmCQlOf47/e9//9OOHTv0888/q379+poyZYrKli1rXR8VFaVnnnlG5cqVk4+PjwoUKKDLly8n2fed0hpLfHy83njjDVWrVk2+vr7y8vLS6tWr77mfu7l27Zrc3NxS1fZu8e7YsUMPPfRQqre3WCwKCAiwbn+v88jX11e9evVSWFiY2rVrp2nTpikiIiLJPtzd3W1+B4CcJufM5AYg22rWrJlmzZqlK1euaMqUKXJ2dlbnzp2t6+Pj4/X222/riy++0L///qu4uDjFxsbec06mu32Qp+Tzzz/X9OnTdeTIEV2+fFk3b95UgQIF0n1s165dk6urq82l0qmJ19PTUwUKFLBJXBo1aqT8+fOnuH2VKlXk5ORkfV2sWDHt3r1bkrR7927Fx8erfPnyNtvExsZa59MaPHiwnnvuOf34448KDQ1V586dbWKSSFwAANmXm5ubWrRooRYtWujVV1/V008/rbFjx6pXr146duyYHn74YT333HN666235Ovrq99++019+/ZVXFycNae483M28UEsdy678xa3tLh8+bLq1KmjRYsWJVlXtGjRe25frVo1VaxYUV27dlWlSpVUtWpV61xGt++jXbt2mjhxYpLtE4sj7dq1U1BQkD766CMVL15cCQkJqlq1apJbCG8//sR85l7HX6RIEZUtW1Zly5bV0qVLVa1aNdWtW1eVK1eWdGturHPnzmnatGkKCgqSq6urQkJC7nn7YlpjeeeddzRt2jRNnTrVOp/Y0KFD77mfex1bYn51L3eL193dPU3bJ/aRuH1qzqPw8HANHjxYq1at0ueff67Ro0drzZo1euCBB6xtz58/n6rzDsiuuFIKQIZ5enqqbNmyqlGjhj755BNt2bJFc+fOta5PTCheeuklrVu3Tjt27FBYWFiaEhfp3knkpk2b1K1bN7Vp00bfffedtm/frldeeSXDicvVq1dT1cfd4s2MxMXJyUlbt27Vjh07rD/79+/XtGnTJElPP/20/vnnH/Xo0UO7d+9W3bp19f7779v0SeICAMgpKleurCtXrki6NTl1QkKC3nvvPT3wwAMqX768Tp8+nWn72rx5c5LXlSpVSrZt7dq1dejQIfn5+VkLN4k/Pj4+qdpfnz59tH79+mSvkkrcx969exUcHJxkH56enjp37pwOHDig0aNH66GHHlKlSpV04cKFtB10KgUGBuqJJ57QqFGjrMs2btyowYMHq02bNqpSpYpcXV1tJmHPLBs3blT79u3VvXt31ahRQ6VLl9bBgwcz1GetWrX0999/yxiToX6qV6+eoac/p/Y8qlWrlkaNGqXff/9dVatW1eLFi63rjhw5ouvXr6tWrVoZOhbAkShKAchU+fLl08svv6zRo0dbnwSSFQlFcn7//XcFBQXplVdeUd26dVWuXLkM36pWs2ZNSdK+ffsy1E/16tX166+/pnvS9Vq1aik+Pl5nzpxJkrgEBARY2wUGBurZZ5/V8uXLNWLECH300Uc2/ezZs4fEBQCQrZw7d07NmzfXwoULtWvXLh09elRLly7VpEmT1L59e0lS2bJldePGDb3//vv6559/tGDBAs2ePTvTYti4caMmTZqkgwcPasaMGVq6dKmGDBmSbNtu3bqpSJEiat++vX799VcdPXpU69ev1+DBg3Xq1KlU7e+ZZ57R2bNn9fTTTye7fsCAATp//ry6du2qP//8U0eOHNHq1avVu3dvxcfHq1ChQipcuLDmzJmjw4cP6+eff9bw4cPTffz3MmTIEH377bf666+/JEnlypXTggULtH//fm3ZskXdunVL1RdwaVWuXDmtWbNGv//+u/bv36/+/fsrKioqQ302a9ZMly9f1t69ezPUz9ixY/XZZ59p7Nix2r9/v3bv3p3slW0pudd5dPToUY0aNUqbNm3S8ePH9eOPP+rQoUM2xdJff/1VpUuXtrllFchpKEoByHSPPfaYnJycrI9TzoqEIjnlypXTiRMntGTJEh05ckTTp0/XihUrMtRn0aJFVbt2betTctJr4MCBiomJUZcuXfTXX3/p0KFDWrBgQZJHC6ekfPny6tatm5566iktX75cR48e1R9//KHx48dr5cqVkqShQ4dq9erVOnr0qLZt26Z169bZJC7Hjh3Tv//+q9DQ0AwdCwAAmcnLy8s6b1Hjxo1VtWpVvfrqq3rmmWf0wQcfSJJq1KihyZMna+LEiapataoWLVqk8ePHZ1oMI0aM0F9//aVatWrpzTff1OTJkxUWFpZsWw8PD/3yyy8qWbKkOnXqpEqVKqlv3766fv16qqcMcHZ2VpEiReTsnPxsKsWLF9fGjRsVHx+vli1bqlq1aho6dKgKFiyofPnyKV++fFqyZIm2bt2qqlWratiwYXrnnXfSffz3UrlyZbVs2VJjxoyRJM2dO1cXLlxQ7dq11aNHDw0ePDhV82+m1ejRo1W7dm2FhYWpadOmCggIUIcOHTLUZ+HChdWxY8dkb5tLi6ZNm2rp0qX65ptvVLNmTTVv3jxNTwW813nk4eGhv//+W507d1b58uXVr18/DRgwQP3797f28dlnn+mZZ57J0HEADufomdYB5GwpPb1u/PjxpmjRouby5cvm3Llzpn379sbLy8v4+fmZ0aNHm6eeespmu9Q8OaVGjRo2T46787Uxxvzvf/8zhQsXNl5eXuaJJ54wU6ZMMT4+Ptb1aX36njHGzJw50zzwwAM2y5J7+l7iE2YS+fj4mPDwcOvrnTt3mpYtWxoPDw/j7e1tGjVqZI4cOZJiHEOGDDFNmjSxvo6LizNjxowxwcHBJn/+/KZYsWKmY8eOZteuXcYYYwYOHGjKlCljXF1dTdGiRU2PHj3Mf//9Z93+7bffNmFhYXc9VgAA8pp7Pa0Nuc/OnTuNn5+fzVMZc5o9e/YYPz8/c/HiRUeHAmSIxZgM3kwLALnctWvXVKFCBX3++edJns6TU8TFxalcuXJavHixHnzwQUeHAwBAthEcHKyhQ4dq6NChjg4FdjRv3jzVqVNH1apVc3Qo6fLTTz8pPj4+xSv6gJyCp+8BwD24u7vr008/zZIJPO3lxIkTevnllylIAQAASOrVq5ejQ8gQpmNAbsGVUgAAAAAAALA7JjoHAAAAAACA3VGUAgAAAAAAgN1RlAIAAAAAAIDdUZQCAAAAAACA3VGUAgAAAAAAgN1RlAIAAAAAAIDdUZQCAAAAAACA3VGUAgAAAAAAgN1RlAIAAAAAAIDd/T85mj1jJLhX9AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 4. Compare distributions\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(12, 4))\n",
    "\n",
    "ax1.set_title(f'Population Distribution\\nMean={population_mean:.3f}, SD={population_std:.3f}')\n",
    "ax1.hist(df['rainfall_inches'], bins=30)\n",
    "ax1.set_xlabel('Rainfall (inches)')\n",
    "ax1.set_ylabel('Frequency')\n",
    "\n",
    "ax2.set_title(f'Sampling Distribution\\nMean={sample_means.mean():.3f}, SD={sample_means.std():.3f}')\n",
    "ax2.hist(sample_means, bins=30)\n",
    "ax2.set_xlabel('Sample Mean Rainfall (inches)')\n",
    "ax2.set_ylabel('Frequency')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e75e4b17",
   "metadata": {},
   "source": [
    "### Interpretation\n",
    "\n",
    "**Shape comparison**: The original rainfall distribution is highly right-skewed, but the sampling distribution of means is approximately normal and symmetric. This is the Central Limit Theorem in action!\n",
    "\n",
    "**Normality**: Yes, the sampling distribution is approximately normal despite the original data being non-normal.\n",
    "\n",
    "**Standard error comparison**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5798baf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical standard error: 0.0569\n",
      "Empirical standard error: 0.0573\n",
      "Difference: 0.0005\n"
     ]
    }
   ],
   "source": [
    "theoretical_se = population_std / np.sqrt(sample_size)\n",
    "empirical_se = sample_means.std()\n",
    "\n",
    "print(f\"Theoretical standard error: {theoretical_se:.4f}\")\n",
    "print(f\"Empirical standard error: {empirical_se:.4f}\")\n",
    "print(f\"Difference: {abs(theoretical_se - empirical_se):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80bc2af7",
   "metadata": {},
   "source": [
    "The theoretical and empirical standard errors match closely, confirming the CLT prediction.\n",
    "\n",
    "**Why CLT matters**: The CLT explains why we can use normal-based statistical methods (like confidence intervals and hypothesis tests) even when our data isn't normally distributed. As long as our sample size is large enough, the sampling distribution of the mean will be approximately normal, allowing us to make valid inferences."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4ecf183",
   "metadata": {},
   "source": [
    "### Bonus: Effect of Sample Size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3d4a818c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1600x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bonus: Different sample sizes\n",
    "sample_sizes = [5, 10, 30, 50]\n",
    "fig, axes = plt.subplots(1, 4, figsize=(16, 4))\n",
    "\n",
    "for idx, n in enumerate(sample_sizes):\n",
    "\n",
    "    sample_means_n = []\n",
    "\n",
    "    for _ in range(1000):\n",
    "        sample = df['rainfall_inches'].sample(n=n, replace=True)\n",
    "        sample_means_n.append(sample.mean())\n",
    "\n",
    "    sample_means_n = np.array(sample_means_n)\n",
    "\n",
    "    axes[idx].hist(sample_means_n, bins=30)\n",
    "    axes[idx].set_xlabel('Sample Mean')\n",
    "    axes[idx].set_ylabel('Frequency')\n",
    "    axes[idx].set_title(f'n={n}\\nSD={sample_means_n.std():.4f}')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44e072a2",
   "metadata": {},
   "source": [
    "**Observation**: As sample size increases, the sampling distribution becomes more normal and has less spread (smaller standard error). Larger samples provide more precise estimates of the population mean."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}