Texas Instruments produces computer chips in production runs of 1 million at a time. It has found that the fraction of defective modules can be very different in different production runs. These differences are caused by small variations in the set-up of each production run. Managers have observed that defective rates are roughly triangular, with a lower bound of 0%, and an upper bound of 50%. Defects more likely to be near 10% than any other single value in their range. (a) Before we test any modules, let’s understand the distribution of de- fects. Simulate at least 2,000 draws from the triang
Texas Instruments produces computer chips in production runs of 1 million at a time. It has found that the fraction of defective modules can be very different in different production runs. These differences are caused by small variations in the set-up of each production run. Managers have observed that defective rates are roughly triangular, with a lower bound of 0%, and an upper bound of 50%. Defects more likely to be near 10% than any other single value in their range. (a) Before we test any modules, let’s understand the distribution of de- fects. Simulate at least 2,000 draws from the triangular distribution and answer the following questions.
1 What is the probability of a defect rate less than 0.25 in this production run?
2 For what number M would you say that the defective rate is equally likely to be above or below M?
3 What is the probability that we will find exactly two defective modules when we test 10 modules from this production run?
(b) Now suppose that we have taken a sample of 10 modules, and 2 of them are defective.
1 What is the conditional probability of a defective rate less than 25% in this production run?
2 For what number M would you say that the defective rate is equally likely to be above or below M?
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