3.

(05.02 MC)

The amount people who pay for cable service varies quite a bit, but the mean monthly fee is $198 and the standard deviation is $37. The distribution is not Normal. Many people pay about $76 for basic cable and about $160 for premium service, but some pay much more. A sample survey is designed to ask a simple random sample of 1,000 cable service customers how much they pay. Let x be the mean amount paid.

Part A: What are the mean and standard deviation of the sample distribution of x? Show your work and justify your reasoning. (4 points)

Part B: What is the shape of the sampling distribution of x? Justify your answer. (2 points)

Part C: What is the probability that the average cable service paid by the sample of cable service customers will exceed $205? Show your work. (4 points) (10 points)