According to the Current Results website, the state of California has a mean annual rainfall of 21 inches, whereas the state of New York has a mean annual rainfall of 55 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample 45 of 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. a. Show the probability distribution of the sample mean annual rainfall for California. This is a graph of a normal distribution with and (to 4 decimals).
b. What is the probability that the sample mean is within 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 inch is for New York in part (c) because the sample size is.