Question

Gateway 2000 Inc. receives large shipments of microprocessors from Intel Corp. It must try to ensure that the proportion of microprocessors that are defective is small. Suppose Gateway samples and tests 5 microprocessors out of a shipment of thousands of these microprocessors. Suppose also that if at least 1 of the microprocessors is defective, the shipment is returned. This sampling and inspection scheme can be modeled as a Binomial process with parameters n and p. Define x = the number of defective microprocessors out of 5 sampled and inspected. Use the spreadsheet named Gateway.

a. Starting in cell A3, moving down, list all possible values for the number of defective microprocessors (out of 5 sampled).

b. Suppose that Intel Corp.'s shipment contains 10% defective microprocessors. Use Excel's built-in function for the Binomial distribution to calculate the probability for each outcome you listed in column A. Start the probability calculations in cell B3 and move down. Also, show that you ensured that the sum of the probabilities of all possible outcomes is 1.

c. Again, suppose that Intel Corp.'s shipment contains 10% defective microprocessors. In cell C11, find the average number of defectives we expect in a sample of 5 microprocessors.

d. Again, suppose that Intel Corp.'s shipment contains 10% defective microprocessors. In cell C13, provide the probability that the entire shipment will be returned (assuming 10% defect rate and 5 microprocessors sampled).

e. In cell C15, calculate the probability that the entire shipment will be kept by Gateway even though the shipment has 10% defective microprocessors assuming 5 microprocessors are sampled.