iii webassignnei sample of 35 years of rainfall for California and a sample of 47 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. A inches Aug4 inches . 1 0 14 18 22 26 30 34 19.9 20.6 21.3 22 22.7 23.4 24.1 39.9 40.5 41.3 42 .427 43.4 44.1 CDO 63 inches k inches 2.11.470.7 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.) (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? part (b), because the standard error is smaller part (c), because the sample size is larger part (c), because the population standard deviation is smaller part (b), because the population standard deviation is smaller