Binomial distribution

Math

Definition

A probability distribution that models the number of successes in a fixed number of independent trials, each with the same probability of success. It requires a fixed number of trials (n), two outcomes per trial, constant probability (p), and independent trials.

Examples

  • The number of heads in 20 coin flips follows a binomial distribution with n = 20 and p = 0.5
  • If 15% of products are defective, the number of defectives in a random sample of 50 is binomial with n = 50, p = 0.15
Key Fact

Mean = np, Standard deviation = √(np(1−p))

Related Terms

Binomial probability Normal distribution Random variables Standard deviation

Study This Concept

Practice binomial distribution with free review games in these units:

AP Statistics Unit 4: Probability Random Variables and Distributions