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An accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10% show small inventory shortages and 5% show large inventory shortages. The firm has devised a new accounting test for which it believes the following probabilities hold:
P(company will pass test | no shortage) = .90
P(company will pass test | small shortage) = .50
P(company will pass test | large shortage) = .20
a. If a company being audited fails this test, what is the probability of a large or small inventory shortage?
b. If a company being audited passes this test, what is the probability of no inventory shortage?
This result applies no matter what the shape of the probability distribution from which the samples are taken. Central Limit Theorem: How Large a Sample?
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