Check My Work (3 remaining) According to the Current Results website, the state of California has a mean annual rainfall of 25 inches, whereas the state of New York has a mean annual rainfall of 37 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. Use z-table. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with E(): = and = (to 4 decimals). b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals) c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals) 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? because the sample size is - Select your answer - The probability of being within 1 inch is greate - Select your answer - for New York in part (c) for California in part (b) Check My Work (3 remaining)