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 (Current Results website, October 27, 2012). 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.
a. Show the probability distribution of the sample mean annual rainfall for California.
b. What is the probability that the sample mean is within 1 inch of the population mean for California?
c. What is the probability that the sample mean is within 1 inch of the population mean for New York?
d. In which case, part (b) or (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?