The Poisson distribution with parameter l approximates the binomial distribution with parameters (n, p) when nS , pS 0, and npS l. Demonstrate this result for the situation where a manufactured lot is known to contain 1% defective items. If a sample of 10 items is taken from the lot, compute the probability of at most one defective item in a sample, first by using the (exact) binomial distribution and then by using the

(approximate) Poisson distribution. Show that the approximation will not be acceptable if the value of p is increased to, say, 0.5.