Question

**Problem 5.51** **Binomial Distribution**: A consumer advocate claims that

**80 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 five cable subscribers is selected**. Assuming independence, use an appropriate formula to **compute the probability that four or more subscribers in the sample are not satisfied with their service**.

**show your work to calculate*** P*(*x* ³ 4) = 1 - *P*(*x* £ 3):

b Suppose that the advocate's claim is true, and suppose that a **random sample of 25 cable subscribers is selected**. Assuming independence, find:

(1) The probability that **15 or fewer** subscribers in the sample are not satisfied with their

service.

(2) The probability that **more than 20 subscribers** in the sample are not satisfied with their

service. **show your work to calculate ***P*(*x* > 20) = 1 - *P*(*x* £ 20) to get your final answer:

(3) The probability that **between 20 and 24 (inclusive) subscribers** in the sample are not

satisfied with their service.

(A) **Minitab instructions**: Go to Calc > select Probability Distributions > select Binomial > select Cumulative probability > Number of Trials insert 25 > Event Probability insert ".8" > Input Constant insert "19." Click OK.

(B) **Minitab instructions**: Go to Calc > select Probability Distributions > select Binomial > select Cumulative probability > Number of Trials insert 25 > Event Probability insert ".8" > Input Constant insert "24." Click OK.

**show your work to calculate ***P*(20 £ x £ 24) = *P*(*x* £ 24) - *P*(*x* £ 19) to get your final answer:

(4) The probability that **exactly 24 subscribers** in the sample are not satisfied with their service.

c Suppose that when we survey 25 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?

#### Top Answer

a. 0.73728 0.01733186954... View the full answer