Question: Many firms utilize sampling plans to control the quality of manufactured items ready for shipment. To illustrate the use of a sampling plan, suppose that a particular company produces and ships electronic computer chips in lots, each consisting of 1000 chips. This company’s sampling plan specifies that quality control personnel will randomly sample 50 chips from each lot and accept the lot for shipping if the number of defective chips in the sample of 50 is less than 5. Of course, the given lot will be rejected if the number of defective chips is found to be 5 or more.

1. Find the probability of accepting a lot if the actual fraction of defective chips in a given lot is equal to 0.]. Place your answer in the space below.
2. To explore the manner in which the actual proportion of defective chips in a lot impacts the probability of a lot being accepted for shipment, compute the lot acceptance probability if the actual fraction of defective chips is equal to each of the following: 0.1, 0.2, 0.3, 0.4, 0.5, . . . 0.8, 0.9. Indicate these probabilities in the table below. What general observation can you make about the likelihood of a lot of this company’s chips being shipped as a function of the proportion of actual defective chips in a lot? Place your response in the space below the table of acceptance probabilities.

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