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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 Spring '05
 DanieleVeneziano
 Statistics, Poisson Distribution, Probability, Probability theory, Poisson process, improper welds

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