Question

4. A company generally purchases large lots of a certain kind of electronic device. A method is used to make a decision, which is to reject a lot if 2 or more defective units are found in a random sample of 100 units. a. [3] What is the probability of rejecting a lot that is 1% defective? b. [3] What is the probability of accepting a lot that is 5% defective?

Answer 1

From the given information, the decision is to reject a lot if 2 or more defective units are found in a random sample of 100 units Probability of defective item, p 0.01 Sample size n-100 The mean number of defective items 1S =100(001) Let Xbe the number of defective items The probability function is, x! x! -1 :x=0,1,2, x! The probability of rejecting a lot that is 1% defective is. P (Rejecting alot) P(finding 2 or more defective items) - P(X22) 1--( e= 2.71828) 1-0.7358 = 10.2642 Therefore, the probability of rejecting a lot that is 1% defective is 0.2642

Probability of defective item, p 0.05 Sample size n-100 The mean number of defective items is, 100(0.05) Let Xbe the number of defective items The probability function is, x! x! The probability of accepting a lot that is 5% defective is, P(Accepting a lot) P(finding less than 2 defective items) - P(X <2) 0! 1! -5 -бе-5 ( 2.71828) e 0.0404 Therefore, the probability of accepting a lot that is 5% defective is 0.0404