Cost of unleaded fuel. According to the American Automobile Association (AAA), the average cost of… 1 answer below »

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 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 , the sample mean cost per gallon.

a. Calculate μ  and σ.

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  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?

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