The average annual precipitation for a large Midwest City is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed.
a. Find the probability that a randomly selected month will have less than 30 inches.
b. Find the probability that the mean of a random selection of 32 months will have a mean less than 30 inches.
c. Does it seem reasonable that one month could have a rainfall amount less than 30 inches? Yes, the probability is slightly more than 40%.
d. Does it seem reasonable that the mean of a sample of 32 months could be less than 30 inches?