The Oil Price Information Center reports the mean price per gallon of regular ga

Question

The Oil Price Information Center reports the mean price per gallon of regular gasoline is $3.79 with a population standard deviation of $0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.

a. What is the standard error of the mean in this experiment?
b. What is the probability that the sample mean is between $3.77 and $3.81?
c. What is the probability that the difference between the sample mean and the population mean is less than 0.01?
d. What is the likelihood that the sample mean is greater than $3.87?

Explanation / Answer

Given xbar=3.79, s=0.18, n=40

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a. What is the standard error of the mean in this experiment?

Standard error of the mean = s/n = 0.18/sqrt(40) =0.028

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b. What is the probability that the sample mean is between $3.77 and $3.81?

P(3.77<xbar<3.81) = P((3.77-3.79)/0.18/sqrt(40) < (xbar-)/(s/n) <(3.81-3.77)/0.18/sqrt(40))

=P(-0.02<Z<0.04)

=0.0239 (check standard normal table)

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d. What is the likelihood that the sample mean is greater than $3.87?

P(xbar>3.87) = P(Z>(3.87-3.77)/0.18/sqrt(40))

=P(Z> 0.09)

= 0.4641(check standard normal table)

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