Probability Distributions: Types, Applications, and Calculations

Probability Distributions

Types of Probability Distributions

Normal Distribution

• Used to model continuous data
• Examples: Heights of people, scientific measurements, test scores

Binomial Distribution

• Used to model discrete data with two possible outcomes
• Examples: Number of heads in a coin toss, number of successes in a series of trials

Poisson Distribution

• Used to model the number of events occurring in a fixed interval of time or space
• Examples: Number of phone calls received per hour, number of earthquakes per year

Applications of Probability Distributions

• Sales success
• Launch of new products
• Bidding for contracts
• Quality control
• Hiring staff
• Experimental trials

Calculating Probabilities

Normal Distribution

• Use a calculator or statistical software
• Formula: P(X < x) = Φ((x - μ) / σ)

Binomial Distribution

• Use a calculator or statistical software
• Formula: P(X = x) = (n! / (x!(n-x)!)) * p^x * (1-p)^(n-x)

Poisson Distribution

• Use a calculator or statistical software
• Formula: P(X = x) = (e^-λ * λ^x) / x!