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 10 randomly selected​ consumers, find the probability that exactly 8 of the 10 consumers recognize the brand name. Also find the probability that the number who recognize the brand name is not 8.

Answer 1

69.81%

Explanation:

We have a binomial problem, where the sample sample size is 10 and p = 80%

Find the probability that exactly 8 of the 10 consumers recognize the brand name, where n = 10 and x = 8

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

Replacing:

P (x = 8) = 10C8 * [(0.8) ^ 8] * [(0.2) ^ (2)]

P (x = 8) = 45 * [(0.8) ^ 8] * [(0.2) ^ (2)]

P = 0.3019

To find the probability that the number recognized by the mark is not 8, it would be

P = 1 - P (x = 8)

P = 1 - 0.3019

P = 0.6981

That is, the probability is 69.81%