A quality inspector for Alpha-Beta Co. is concerned about the quality of the batch of several thousand blank DVD disks which his company produced this week and is preparing to ship. If he uses an acceptance sampling plan of n = 5 and c = 2, what is the probability that, if this batch is 40 percent defective, it will be rejected and receive 100 percent inspection prior to shipment?
A) .1270
B) .2730
C) .3174
D) .6826
E) .7270

Question

Quizplus · Accepted Answer

Using binomial probability formula, we get:

P(reject) = P(X >= 2) = 1 - P(X < 2) = 1 - [P(X = 0) + P(X = 1)]

where X is the number of defective disks in a sample of 5.

P(X = 0) = (0.6)^5 = 0.07776
P(X = 1) = 5(0.4)(0.6)^4 = 0.2592

P(reject) = 1 - (0.07776 + 0.2592) = 0.66304

Therefore, the probability of the batch being rejected and receiving 100 percent inspection prior to shipment is 0.66304, which is closest to 0.3174 (option C).

A Quality Inspector for Alpha-Beta Co