The average price of a gallon of unleaded regular gasoline was reported to be $3.44 in northern Kentucky. Use this price as the population mean, and assume the population standard deviation is $0.30.

a) What is the probability that the mean price for a sample of 50 service stations is within $.06 of the population mean?

b) What is the probability that the mean price for a sample of 100 service stations is within $.06 of the population mean?