25. Money magazine reported that the average price of a gallon of gasoline in the United States during the first quarter of 2001 was $1.46 (Money,August 2001).Assume the price reported by Money is the population mean, and the population standard deviation is σ  $.15.

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

b. What is the probability that the mean price for a sample of 50 gas stations is within $.03 of the population mean?

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

d. Would you recommend a sample size of 30, 50, or 100 to have at least a .95 probability that the sample mean is within $.03 of the population mean?