Gateway 2000 Inc. receives large shipments of microprocessors from Intel Corp….

Directions: Answer the question below by
placing the appropriate graph and/or answers in the designated cells of the
spreadsheet (see separate spreadsheet attachment).

Question 4

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.

4a. Starting in cell A3, moving down, list
all possible values for the number of defective microprocessors (out of 5
sampled).

4b. 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.

4c. 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.

4d. 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).

4e. 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.