Phoenix water is provided to approximately 1.4 million people, who are served through more than 362,000 accounts (phoenix.gov/WATER/wtrfacts.html). All accounts are metered and billed monthly. The probability that an account has an error in a month is 0.001, and accounts can be assumed to be independent.
(a) What is the mean and standard deviation of the number of account errors each month?
(b) Approximate the probability of fewer than 350 errors in a month.
(c) Approximate a value so that the probability that the number of errors exceeds this value is 0.05.
(d) Approximate the probability of more than 400 errors per month in the next two months. Assume that results between months are independent.