The amount people who pay for cable service varies quite a bit, but the mean monthly fee is $142 and the standard deviation is $29. 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 1,500 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 $143? Show your work. (4 points)

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Normal