SOLUTION: The Oil Price Information Center of greater Houston reports the mean price per gallon of regular gasoline is $3.00 with a population standard deviation of $0.18. Assume a random sa
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Question 617681: The Oil Price Information Center of greater Houston reports the mean price per gallon of regular gasoline is $3.00 with a population standard deviation of $0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gas is computed.
a. What is the standard error of mean in this experiment?
b. What is the probability that the sample mean is between $2.98 and $3.02?
c. What is the probability that the difference between the sample mean and the population mean is leass than .01?
d. What is the likelihood the sample mean is greater than $3.08?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Oil Price Information Center of greater Houston reports the mean price per gallon of regular gasoline is $3.00 with a population standard deviation of $0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gas is computed.
a. What is the standard error of mean in this experiment?
std of the sample means = 0.18/sqrt(40) = 0.0285
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b. What is the probability that the sample mean is between $2.98 and $3.02?
z(2.98) = (2.98-3.00)/0.0285 = -0.7018
z(3.02) = +0.7018
Prob = normalcdf(-0.7018,+0.7018) = 0.5172
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c. What is the probability that the difference between the sample mean and the population mean is leas than .01?
Find the z-values of 2.99 and 3.01
Then find the probabilitity that z is between those two z-values.
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d. What is the likelihood the sample mean is greater than $3.08?
z(3.08) = (3.08-3.00)/0.0285 = 2.8070
P(x-bar > 3.08) = P(z > 2.8070) = normalcdf(2.8070,100) = 0.0025
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cheers,
Stan H.
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