A Quality Inspector for Alpha-Beta Co.is concerned about the quality of the batch of several thousand Gizmos 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% defective,it will be rejected and receive 100% inspection prior to shipment?
A)0.1270
B)0.2730
C)0.3174
D)0.6826
E)0.7270

Question

Quizplus · Accepted Answer

The probability of rejecting the batch can be found using binomial distribution with parameters n = 5, p = 0.4 (since the batch is 40% defective) and c = 2 (since the acceptance number is 2).

P(reject batch) = P(X ≥ c) = 1 - P(X < c)
where X ~ Bin(5, 0.4)

Using binomial tables or a calculator, we get:
P(reject batch) = 0.3174

Therefore, the best choice is C.