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?

Question

Veronica Jordan

Mathematics

28 June, 10:01

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?

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Sheppard · 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