Probability_and_Statistics_Project

This repository contains Python implementations of various probability and statistics concepts. Each script is structured to solve a specific statistical problem.

Project Overview

The repository includes the following problem statements:

1. Confidence Interval Calculation (confidence_interval.ipynb)

• Computes a 90% confidence interval for customer satisfaction data.
• Uses scipy.stats.norm.ppf to calculate the margin of error.

2. Probability Calculation for Car Speeds (probability_car_speeds.ipynb)

• Calculates the probability of a randomly selected car exceeding a given speed.
• Uses the normal distribution (mean = 75 km/h, std dev = 15 km/h).

3. Rainfall and Flood Probability Analysis (rainfall_flood_analysis.ipynb)

• Loads the kerala.csv dataset.
• Analyzes rainfall trends in June and July.
• Computes conditional probabilities of flooding based on rainfall data.

4. Wine Dataset Sampling (wine_dataset_analysis.ipynb)

• Loads the wine dataset from the sklearn library.
• Converts it into a Pandas DataFrame.
• Generates a random sample of size 50.
• Computes Z-critical value, margin of error, and confidence interval for alcohol content at a 95% confidence level.

Installation & Requirements

Ensure you have the following dependencies installed:

pip install pandas numpy scipy scikit-learn
Usage
Navigate to the scripts directory and run the individual scripts. Example:

bash
Copy
Edit
cd scripts
python confidence_interval.py

Datasets
kerala.csv - Contains historical rainfall data for Kerala, India.
Wine dataset - Imported from sklearn.datasets.load_wine().

### Dataset Descriptions:
1. **Kerala Rainfall Dataset (`kerala.csv`)**  
   - Columns: Year, monthly rainfall data (Jan-Dec), annual rainfall, and flood indicator (YES/NO).
   - Purpose: Analyze rainfall trends and predict flood probabilities.

2. **Wine Dataset**  
   - Source: `sklearn.datasets.load_wine()`
   - Contains chemical composition of wines.
   - Used for statistical inference on alcohol content.