According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in August 2010 was $2.78 (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-bar, the sample mean cost per gallon.
a. Calculate σx-bar and σx-bar.
b. What is the approximate probability that the sample has a mean fuel cost between $2.78 and $2.80?
c. What is the approximate probability that the sample has a mean fuel cost that exceeds $2.80?
d. How would the sampling distribution of x-bar 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?