Dell Computers receives large shipments of microprocessors from Intel Corp. It must try to ensure the proportion of microprocessors that are defective is small. Suppose Dell decides to test five microprocessors out of a shipment of thousands of these microprocessors. Suppose that if at least one of the microprocessors is defective, the shipment is returned. If Intel and Dell agree that Intel will not provide more than 5% defective chips, calculate the probability that the entire shipment will be returned even though only 5% are defective.
A) 0.2262
B) 0.3478
C) 0.4564
D) 0.1812

Question

Quizplus · Accepted Answer

The probability that a shipment will be returned is the same as the probability of finding at least one defective chip in the sample of five. This can be calculated as 1 minus the probability of finding no defective chips in the sample. If the defect rate is 5%, the probability of a chip being non-defective is 95%, or 0.95. For five chips, the probability that all are non-defective is $0.95^5$. Thus, the probability of finding at least one defective chip is $1 - 0.95^5 = 1 - 0.7738 = 0.2262$.

Dell Computers Receives Large Shipments of Microprocessors from Intel Corp