Question

A brand name has an 80​% recognition rate. If the owner of the brand wants to verify that rate by beginning with a small sample of 15 randomly selected​ consumers, find the probability that exactly 12 of the 15 consumers recognize the brand name. Also find the probability that the number who recognize the brand name is not 12.

Answer 1

74.99%

Explanation:

We have a binomial problem, where the sample sample size is 15 and p = 80%

Find the probability that exactly 12 of the 15 consumers recognize the brand name, where n = 15 and x = 12

P (x) = nCx * [(p) ^ x] * [(1 - p) ^ (n-x)]

Replacing:

P (x = 12) = 15C12 * [(0.8) ^ 12] * [(0.2) ^ (3)]

P (x = 12) = 455 * [(0.8) ^ 12] * [(0.2) ^ (3)]

P = 0.2501

To find the probability that the number recognized by the mark is not 12, it would be

P = 1 - P (x = 12)

P = 1 - 0.2501

P = 0.7499

That is, the probability is 74.99%