Cost of unleaded fuel. According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65 (AAA Fuel Gauge Report). Assume that the standard deviation of such costs is $.15. Suppose that a random sample of n = 100 gas stations is selected from the population and the cost per gallon of regular unleaded fuel is determined for each. Consider x, the sample mean cost per gallon.

a. Calculate mx and sx.

b. What is the approximate probability that the sample has a mean fuel cost between $3.65 and $3.67?

c. What is the approximate probability that the sample has a mean fuel cost that exceeds $3.67?

d. How would the sampling distribution of x change if the sample size n were doubled from 100 to 200? How do your answers to parts b and c change when the sample size is doubled?