Question

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 41 inches. Assume that the standard deviation for both states is 4 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 graph of a normal distribution with E(x) and the variance (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? The probability of being within 1 inch is (greater or smaller) for New York in part (c) because the sample size is (greater or smaller)

Answer 1

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