STA 2023Section 4.2Binomial Distributions

Binomial Experiments

Example 1: Determine if the following probability experiment is a binomial experiment are not.

An experiment in which a basketball player who historically makes 80% of his free throws is asked to shoot three free throws, and the number of made free throws is recorded. Yes

A probability experiment in which three cards are drawn from a deck without replacement and the number of aces is recorded. No.

Binomial Probability Formula

On the calculator

Example 4: A survey indicates that 21% of men in the U.S. consider fishing their favorite leisure-time activity. You randomly select six U.S. men and ask them if fishing is their favorite leisure-time activity. Find the following probabilities.

Exactly two respond yes. Answer: .258

At least two of them respond yes. Answer: .369

Fewer than two of the respond yes. Answer: .631

Constructing a Binomial Distribution A binomial distribution is a special type of a

discrete probability distribution. We construct the binomial distribution the same way we construct any discrete probability distribution.

Example 5: Twenty-six percent of people in the United States with Internet access go online to get news. A random sample of five Americans with Internet access is selected and asked if they get the news online. Construct the binomial distribution for this situation.

Mean, Variance, and Standard Deviation