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.

74.99%

Step-by-step 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%

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