Northern Kentucky

The average price of a gallon of unleaded gasoline was reported to be $2.34 in northern Kentucky. Use the price as the population mean and assume the population standard deviation is $0.20.

a. What is the probability that the mean price for a sample of 30 services stations is within $.03 of the population mean?

b. What is the probability the mean price for a sample of 50 services station is within $.03 of the population mean?

c. What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean?

d. Which if any of the sample sizes in parts (a) (b) and (c) would you recommend to have at least a .95 probability that the sample mean is within $.03 of the population mean?