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 45 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. A inches A inches 39.9 40.6 41.3 42 42.7 43.4 44.1 2.1 1.4 0.7 0 L4 2.1 O @O (D 6); inches A inches 19.9 20.5 21.3 22 22.7 23.4 24.1 (90 (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 (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.) :1 (d) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? 0 part (c), because the sample size is larger 0 part (b), because the standard error is smaller 0 part (c), because the population standard deviation is smaller 0 part (b), because the population standard deviation is smaller