Homework SourseAcceptance sampling is an important quality control techniqu
Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 9% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 12%. UseTable 1.
What is the probability that the production machines will be adjusted if the batch consists of 72 items?(Round intermediate calculations to 4 decimal places,
| Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 9% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 12%. UseTable 1. |
Solution
(a) P(phat>0.12) = P((phat-p)/sqrt(p*(1-p)/n) >(0.12-0.09)/sqrt(0.09*(1-0.09)/72))
=P(Z>0.89) =0.1867 (from standard normal table)
-----------------------------------------------------------------------------------------------------------------
(b)P(phat>0.12) = P((phat-p)/sqrt(p*(1-p)/n) >(0.12-0.09)/sqrt(0.09*(1-0.09)/84))
=P(Z>0.96) =0.1685 (from standard normal table)
