Dell Computers receives large shipments of microprocessors (chips) from Intel Corp. It must try to ensure that the proportion of defective chips is small and has contracted to keep the proportion of defective chips at 5% or less. Suppose that Dell tests 25 chips (with replacement) out of a shipment of thousands. a) What is the probability of obtaining at least three defects in the sample, if the entire shipment has 5% defectives? If a sample results in at least three defects, does it appear that Intel has provided a shipment which is consistent with the contract? Briefly explain, using the calculated probability.
b) For the shipment described in part a, find the expected number of sampled chips that are defective and the standard deviation of the number of sampled chips that are defective.
c) Suppose that 20% of the entire shipment is defective. What is the probability that more than 17 chips in the sample are good (not defective)?