sample of 31 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. -21-14-07 0 0.7 14 21 199 200 21.3 22 22.7 234 24.1 inches inches Assume that the standard deviation for both states is 4 inches. A ^^ inches 39.9 40.6 413 42 42.7 434 44.1 @O 10 14 18 22 (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) 26 30 34 inches

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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 31 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken.
(a) Show the probability distribution of the sample mean annual rainfall for California.
-2.1-14-0.7 0 0.7 1.4 2.1
199 200 21.3 22 22.7 234 24.1
inches
inches
^^
inches
39.9 40.6 41.3 42 42.7 434 44.1
@0
10 14 18 22 26
(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)
(a) 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?
30 34
inches
Transcribed Image Text: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 31 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. -2.1-14-0.7 0 0.7 1.4 2.1 199 200 21.3 22 22.7 234 24.1 inches inches ^^ inches 39.9 40.6 41.3 42 42.7 434 44.1 @0 10 14 18 22 26 (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) (a) 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? 30 34 inches
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