According to the Current Results website, the state of California has a mean annual rainfall of25inches, whereas the state of New York has a mean annual rainfall of38inches. Assume that the standard deviation for both states is4inches. A sample of30years of rainfall for California and a sample of45years of rainfall for New York has been taken. Usez-table.

a.Show the probability distribution of the sample mean annual rainfall for California.

This is a normal probability distribution withE(x)=and0x=(to4decimals). 

b.What is the probability that the sample mean is within1inch of the population mean for California?

(to4decimals)

c.What is the probability that the sample mean is within1inch of the population mean for New York?

(to4decimals)