LK My Work 12 remaining) 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 3 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal places. (a) Show the sampling distribution of the sample mean annual rainfall for California. E(X) 02 California inches inches (b) Show the sampling distribution of the sample mean annual rainfall for New York. E(X) New York inches inches (c) in which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why? The standard error is - Select your answer for New York because the sample size is - Select your answer. than for California