The average price per gallon of unleaded regular gasoline was reported to be $2.
ID: 3432543 • Letter: T
Question
The average price per gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky. Use this price as the population mean, and assume that the population standard deviation is $0.20.
1. For a random sample of 64 service stations, find the standard deviation of the sampling distribution of the sample mean.
2. What is the probability that the mean price for a sample of 64 service stations is within $0.03 of the population mean?
3. For a random sample of 100 service stations, find the standard deviation of the sampling distribution of the sample mean.
4. What is the probability that the mean price for a sample of 100 service stations is within $0.03 of the population mean?
Explanation / Answer
1.
standard deviation of the sampling distribution of the sample mean.= population std deviation/sqrt(n) = 0.2/sqrt(64) = 0.2/8 = 0.025
2.
t-statistics =0.03/0.025 = 1.2
Probability = P( -1.2 < z < 1.2) = 0.7698
3.
standard deviation of the sampling distribution of the sample mean.= population std deviation/sqrt(n) = 0.2/sqrt(100) = 0.2/10 = 0.02
4.
t-statistics =0.03/0.02 = 1.5
Probability = P( -1.5 < z < 1.5) = 0.8663
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