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. 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 "3." Click OK.
Paste your Minitab results here and then 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. 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 "15." Click OK.
Paste your Minitab results here:
(2). The probability that more than 20 subscribers in the sample are not satisfied with their
service. 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 "20." Click OK.
Paste your Minitab results here and then 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 "20." 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.
Paste each of your Minitab results here and then 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.
Paste your Minitab results here:
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?
Explain your answer here: