Cost of unleaded fuel. According to the American Automobile Association (AAA), the average...

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  and.

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b. What is the approximate probability that the sample has a mean fuel cost between $2.78 and $2.80?

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c. What is the approximate probability that the sample has a mean fuel cost that exceeds $2.80?

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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 is doubled?

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b. What is the approximate probability that the sample has a mean fuel cost between $2.78 and $2.80?

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c. What is the approximate probability that the sample has a mean fuel cost that exceeds $2.80?