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 5 cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that 4 or more subscribers in the sample are not satisfied with their service. (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

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 5 cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that 4 or more subscribers in the sample are not satisfied with their service. (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

(b) Suppose that the advocate's claim is true, and suppose that a random sample of 20 cable subscribers is selected. Assuming independence, find: (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

Binomial, n =_________ , p = ___________

1. The probability that 10 or fewer subscribers in the sample are not satisfied with their service.

Probability             

2. The probability that more than 15 subscribers in the sample are not satisfied with their service.

Probability ___________   

3. The probability that between 15 and 18 (inclusive) subscribers in the sample are not satisfied with their service.

Probability __________

4. The probability that exactly 18 subscribers in the sample are not satisfied with their service.

Probability _______________

(c) Suppose that when we survey 20 randomly selected cable television subscribers, we find that 10 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. (Round your answer to 4 decimal places.)

(Click to select)  Yes  No  ; if the claim is true, the probability that 10 or fewer  (Click to select)  are  are not  satisfied is only  .

Answer 1

Solution:

(a) Suppose that the advocate's claim is true, and suppose that a random sample of 5 cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that 4 or more subscribers in the sample are not satisfied with their service.

Answer: We have to find:

Using the binomial probability distribution function, we have:

(b) Suppose that the advocate's claim is true, and suppose that a random sample of 20 cable subscribers is selected. Assuming independence, find: (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

Binomial,

1. The probability that 10 or fewer subscribers in the sample are not satisfied with their service.

Explanation:

The excel function to find this probability is:

2. The probability that more than 15 subscribers in the sample are not satisfied with their service.

Explanation:

The excel function to find this probability is:

3. The probability that between 15 and 18 (inclusive) subscribers in the sample are not satisfied with their service.

Explanation:

The excel function to find this probability is:

4. The probability that exactly 18 subscribers in the sample are not satisfied with their service.

Explanation:

The excel function to find this probability is:

(c) Suppose that when we survey 20 randomly selected cable television subscribers, we find that 10 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. (Round your answer to 4 decimal places.)

No; if the claim is true, the probability that 10 or fewer are not satisfied is only 0.0139.