The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was $273 . Use this price as the population mean and assume the population standard deviation of...

The CPA Practice Advisor reports that the mean preparation fee for  federal income tax returns was $273 . Use this price as the population mean and assume the population standard deviation of preparation fees is 100 . Use
z-table.

Round your answers to four decimal places.

a.
What is the probability that the mean price for a sample of 30 federal income tax returns is within 16 of the population mean?

b.
What is the probability that the mean price for a sample of 50 federal income tax returns is within 16 of the population mean?

c.
What is the probability that the mean price for a sample of 100 federal income tax returns is within 16 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 16 of the population mean?