Industrial quality control programs often include inspection of incoming materia
ID: 2924239 • Letter: I
Question
Industrial quality control programs often include inspection of incoming materials from suppliers. If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them. A lot might be judged acceptable if one or fewer defective parts are found among those inspected. Otherwise, the lot is rejected and returned to the supplier. Use technology or Appendix Table 9 to find the probability of accepting lots that have each of the following. (Hint: Identify success with a defective part. Round your answers to three decimal places.)
(a) 5% defective parts
P(lot will be accepted) =
(b) 10% defective parts
P(lot will be accepted) =
(c) 25% defective parts
P(lot will be accepted) =
Explanation / Answer
P(X = x) = nCx * px * (1 - p)n-x
a) p = 0.05
n = 20
P(lot will be accepted) = P(X < 1)
= P(X = 0) + P(X = 1)
= 20C0 * 0.050 * 0.9520 + 20C1 * 0.051 * 0.9519
= 0.736
b) p = 0.10
n = 20
P(lot will be accepted) = P(X < 1)
= P(X = 0) + P(X = 1)
= 20C0 * 0.100 * 0.9020 + 20C1 * 0.101 * 0.9019
= 0.270
c) p = 0.25
n = 20
P(lot will be accepted) = P(X < 1)
= P(X = 0) + P(X = 1)
= 20C0 * 0.250 * 0.7520 + 20C1 * 0.251 * 0.7519
= 0.024