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 32 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Describe the probability distribution of the sample mean annual rainfall for California by specifying its distribution form and parameters. (Round your answers to four decimal places as needed.) This is a ---Select--- distribution with E(X) = and σ- = X (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 O part (c), because the population standard deviation is smaller O part (c), because the sample size is larger O part (b), because the population standard deviation is smaller

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