Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate about 5% defective items. Let X be the number of defective items in a sample without replacement of size n = 10. Suppose the factory returns the shipment if X ≥ 2.
(a) Obtain the probability that the factory returns a shipment of items which has 5% defective items.
(b) Suppose the shipment has 10% defective items. Obtain the probability that the factory returns such a shipment.
(c) Obtain approximations to the probabilities in parts (a) and (b) using appropriate binomial distributions.