Homework Set #2 Problem 1 A machine to detect improper welds in a fabricating shop detects 80 percent of all improper welds, but it also incorrectly indicates an improper weld on 5 percent of all satisfactory welds. Past experience indicates that 10 percent of all welds are improper. (a) What is the probability that a weld that the machine indicates to be defective is in fact satisfactory? (b) What is the probability that a weld which the machine indicates to be satisfactory is in fact defective? (c) Compare the probabilities in (a) and (b) and comment on their relative magnitudes. Problem 2 The service stations along a highway are located according to a Poisson process in space, with an average of 1 service station in 10 miles. Because of a gas shortage, there is a probability of 0.3 that a service station would have no gasoline available. Assume that the availabilities of gasoline at different service stations are statistically independent.
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