According to the Current Results website, the state of California has a mean annual rainfall of 23 inches, whereas the state of New York has a mean annual rainfall of 51 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use z-table.

a. Show the probability distribution of the sample mean annual rainfall for California. (to 4 decimals).

b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals)

c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals)