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# According to the American Automobile Association, the average cost of a gallon

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According to the American Automobile Association, the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was \$3.65. Assume that the standard deviation of such costs is \$0.16. Suppose that a random sample of n = 75 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) Find E(X) and SD(X).

b) What is the probability that the sample has a mean fuel cost between \$3.63 and \$3.66?

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

d) How would the sampling distribution of a change if the sample size n were doubled from 75 to 150? How do your answers to parts b and c change when the sample size is doubled?

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## [Solved] According to the American Automobile Association, the average cost of a gallon

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### Answers to According to the American Automobile Association.

A) Given Sample mean X follows a normal distribution with mean And standard deviation Then , Follows standard normal distribution. B) P(3.63 < x< 3.66) If sample mean is doubled n= 150 ...

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