Question

A supermarket sells two flavors of cereal: a fruit flavor and a chocolate flavor. In a market survey, the event that a customer says he or she is willing to buy the fruit flavor is considered a success. Records for the past 5 years show that an average of 71% of the customers buy the fruit-flavored cereal. If 20 cereal buying customers walk into the supermarket, what is the probability that at the most 19 of them will buy the fruit-flavored cereal?

Answer 1

This is a binomial distribution.
p = 0.71, q = 1 - p = 1 - 0.71 = 0.29, n = 20

P(x ≤ 19) =1 - P(x = 20) = 1- 20C20 x (0.71)^(20 - 20) x (0.29)^20 = 1 - 0.29^20 = 1 - 0 = 1