A computer factory receives large shipments of chips. Different shipments have d
ID: 3240228 • Letter: A
Question
A computer factory receives large shipments of chips. Different shipments have different levels of quality. In order to decide whether to accept a particular shipment, inspectors randomly select a sample of 20 computer chips and test them;if at least two chips in the sample are defective, the shipment is returned. Suppose a very large shipment arrives in which 5% of the computer chips are defective. Let X be a random variable representing the number of defective chips in a random sample of 20. a. Explain why X may be treated as a binomial random variable: Identify n (the number of trials): Specify, in words, which event would be defined as a "success". Explain why the trials may be considered independent: Calculate rho, the probability of a success: b. What is the probability that this shipment is accepted? (Use a table or the formula). c. What is the expected value of the number of defective chips in this sample? d. Fill in the blanks: "For a large shipment contains 5,000 computer chips, the average number of defective items in this sample would be approximately equal to ________ computer chips"Explanation / Answer
a. X must be treated as binomial random variable because we are given the necessary parameters (i) sample size =20 (ii) probability of success = 0.05 to satisfy binomial variable condition.
(i) Identify n = 20
(ii) Success is finding number of defective chips
(iii) The trial may be considered independent because selection of computer chips are totally random here.
b. Probability that shipment is accepted when there are less than 2 defective pieces in the given container.
Pr (Accepted) = Pr(0) + Pr(1) = 20C0 (0.05)0 (0.95)20 + 20C1 (0.05)1 (0.95)19 = 0.3585 + 0.3774 = 0.736
(iv) Excepted value of defective chips in the sample = 20 * 0.05 = 1
(v) When shipment contains 5000 computer chips, average number of defective items = 5000 * 0.05 = 250
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