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) What are the mean and standard deviation of the sampling distribution of¯x ?

(b) Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds $55.

(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 $55.