Question

According to the Current Results website, the state of California has a mean annual rainfall of 20 inches, whereas the state of New York has a mean annual rainfall of 35 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 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  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  inch of the population mean greater? Why?

The probability of being within 1 inch is - Select your answer -greater/lower 5 for New York in part (c) because the sample size is - Select your answer -larger/smaller.

Answer 1

d) The probability of being within 1 inch is greater for New York in part c because the sample size is larger.