A machine is shut down for repairs if a random sample of 100 items selected from the daily output of the machine reveals at least 15% defectives. (Assume that the daily output is a large number of items.)
Suppose that a random sample of 20 items is selected from the machine. If the machine produces 5% defectives, find the probability that the sample will contain at least three defectives, by using the following methods:
(a) the normal approximation to the binomial (Round your answer to four decimal places.)