📊 Probability Distribution Calculator

🎯 Getting Started

Select a distribution type and enter parameters to calculate probabilities:

• Normal Distribution: Enter mean (μ) and standard deviation (σ), then use the slider to find probabilities for specific Z-scores
• Binomial Distribution: Calculate probability of k successes in n trials with probability p
• Poisson Distribution: Calculate probability of k events occurring given rate λ (lambda)

📐 Normal Distribution

The most common continuous probability distribution (bell curve):

• Mean (μ): Center of the distribution
• Standard Deviation (σ): Measure of spread
• Z-Score: Number of standard deviations from mean: Z = (X - μ) / σ
• P(Z ≤ z): Cumulative probability (area under curve to the left)
• P(Z > z): Right tail probability (1 - P(Z ≤ z))

💡 Use the interactive slider to visualize how probability changes with Z-score

🎲 Binomial Distribution

Probability of k successes in n independent trials:

• n (trials): Number of independent experiments
• p (probability): Probability of success on each trial (0 to 1)
• k (successes): Number of successful outcomes
• Example: Probability of getting exactly 7 heads in 10 coin flips

⚡ Poisson Distribution

Probability of k events in a fixed interval:

• λ (lambda/rate): Average number of events per interval
• k (events): Number of events to calculate probability for
• Example: If a store averages 5 customers per hour (λ=5), what's the probability of exactly 3 customers in the next hour?

📊 Understanding Results

• P(X = k): Probability of exactly k occurrences
• P(X ≤ k): Cumulative probability (k or fewer)
• P(X > k): Probability of more than k occurrences