The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 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 46 years of rainfall for New York has been taken.
(a) Show the probability distribution of the sample mean annual rainfall for California.
inches
inches
10
14
18
22
26
30
34
19.9 20.6 21.3 22 22.7 23.4 24.1
A
inches
inches
39.9 40.6 41.3 42 42.7 43.4 44.1
-2.1-1.4 -0.7 0
0.7 1.4 2.1
(b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)
(c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)