A consumer advocate claims that 75 percent of cable television subscribers are n

Question

A consumer advocate claims that 75 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue. (a) Suppose that the advocate's claim is true, and suppose that a random sample of 4 cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that 3 or more subscribers in the sample are not satisfied with their service. (b) Suppose that the advocate's claim is true, and suppose that a random sample of 20 cable subscribers is selected. Assuming independence, find: The probability that 15 or fewer subscribers in the sample are not satisfied with their service. The probability that more than 16 subscribers in the sample are not satisfied with their service. The probability that between 16 and 18 (inclusive) subscribers in the sample are not satisfied with their service. The probability that exactly 18 subscribers in the sample are not satisfied with their service. (c) Suppose that when we survey 20 randomly selected cable television subscribers, we find that 15 are actually not satisfied with their service. Using a probability you found in this exercise as the basis for your answer, do you believe the consumer advocate's claim? Explain.

Explanation / Answer

a) we need to find 4C3*(0.75)3(0.25)+4C4*(0.75)4 = 0.7383

b) 2. we need to find 20C17*(0.75)17(0.25)3 +20C18*(0.75)18(0.25)2 + 20C19*(0.75)19(0.25) + 20C20*(0.75)20 = 0.2252

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