The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $38 and the standard deviation is $10. The distribution is not Normal: many households pay a base rate for low-speed access, but some pay much more for faster connections. A sample survey asks an SRS of 500 households with Internet access how much they pay. Let x– be the mean amount paid.

(a) Explain why you can’t determine the probability that the amount a randomly selected household pays for access to the Internet exceeds $39.

(b) What are the mean and standard deviation of the sampling distribution of x–?

(c) What is the shape of the sampling distribution of x–?

Justify your answer.

(d) Find the probability that the average fee paid by the sample of households exceeds $39. Show your work.