You may need to use the appropriate appendix table or technology to answer this question. 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 35 years of rainfall for California and a sample of 48 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. inches inches inches -21-14 -07 0 07 14 21 39.9 40.6 41.3 42 42.7 434 441 199 20.6 21.3 22 22.7 234 241 o O @ (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.) 1.0000 X (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.) oo x