Question

A manufacturer receives a lot with 100 parts from a vendor. The lot will be unacceptable if it
contains five or more parts that are defective. The manufacturer is going to randomly select K parts from the lot
and the lot will be accepted if no defective parts are found in the sample.
(a) How large does K have to be to ensure that the probability that the manufacturer accepts an unacceptable lot....


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Answer 1

A manufacturer receives a lot with 100 parts from a vendor. The lot will be unacceptable if it
contains five or more parts that are defective. The manufacturer is going to randomly select K parts from the lot
and the lot will be accepted if no defective parts are found in the sample.
(a) How large does K have to be to ensure that the probability that the manufacturer accepts an unacceptable lot
is less than 0.l0? (Note that the probability of accepting an unacceptable lot will be largest when the number
of defectives in the lot is the smallest permissible under the definition of “an unacceptable lot,” namely 5.)
(b) The binomial distribution can be used as an approximation in this case. Assume that K parts are now
sampled with replacement and answer the same question as in (a). (The binomial distribution is technically
not the proper distribution in this case, but its computations are easier and so might be used as a first attempt.)
(c) The answer in (a) is thought to be too high to be practically useful. Instead the manufacturer inspects ten
parts from the lot. Find the probability that the manufacturer accepts an unacceptable lot with 5 defective
parts, with 10 defective parts, and with 15 defective parts.