The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky (The Cincinnati Enquirer, January 21, 2006). Use this price as the population mean, and assume the population standard deviation is $.20.
a. What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean?
b. What is the probability that the mean price for a sample of 50 service stations 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?