A sampling plan states that if 20 incoming bolts are checked and 2 or less defective bolts are discovered,the lot will be rejected. If an incoming lot is 10 percent defective,what is the probability of rejecting the lot?
A)0
B)1
C)0.323
D)0.667

Question

Quizplus · Accepted Answer

Since the lot is 10% defective, this means there are 10 defective bolts in a lot of 100 bolts. We can assume that the lot contains 1000 bolts (just to have a larger sample size), so there would be 100 defective bolts in the lot. 
To calculate the probability of the lot being rejected, we need to use the binomial distribution.

P(rejecting the lot) = P(2 or less defective bolts out of 20)

= P(X ≤ 2), where X ~ B(20,0.10)

Using a binomial distribution table, we find:

P(X ≤ 2) = 0.323

Therefore, the probability of rejecting the lot is 0.323, which is answer choice C.

A Sampling Plan States That If 20 Incoming Bolts Are