Question

According to the Current Results website, the state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 52 inches. Assume that the standard deviation for both states is 5 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 ________ and standard deviation _______ (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)

Answer 1

a) This is a graph of a normal distribution with mean =22 inch and standard deviation =5/sqrt(30)=0.9129

b) sample mean is within 1 inch of the population mean for California

=P(-1/0.9129<Z<1/0.9129)=0.8643-0.1357=0.7286 ( please try 0.7287 if this comes wrong and revert)

c) probability that the sample mean is within 1 inch of the population mean for New York

=P(-1/0.7454<Z<1/0.7454)=P(-1.34<Z<1.34)=0.9099-0.0901=0.8198