The average price of a gallon of unleaded regular gasoline was reported to be $3.13 in Illinois (http://www.cincygasprices.com).

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 your recommend to have at least a .95 probability that the sample mean is within $.03 of the population mean?

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