A very large batch of components has arrived at a distributor. The batchcan be characterized as accept-able only if the proportion of defective components is at most . 10. The distributor decides to randomly select 10components and to accept the batch only if the number of defectivecomponents in the sample is at most 2. a. What is the probability that the batch will be accepted when theactual proportion of defectives is .01? .05? .10? .20? .25?b. Let p denote the actual proportion of defectives in the batch. Agraph of P(batch is accepted) as a function of p, with p on thehorizontal axis and P(batch is accepted) on the vertical axis, is called the operating characteristic curve for the acceptance sampling plan. Use the results of part (a) to sketch this curve for 0≤p≤1. c. Repeat parts (a) and (b) with "1" replacing "2" in the acceptance sampling plan.d. Repeat parts (a) and (b) with "15" replacing "10" in the acceptance sampling plan.e. Which of the three sampling plans, that of part (a), (c), or (d), appears most satisfactory, and why?
A very large batch of components has arrived at a distributor. The batch
can be characterized as accept-able only if the proportion of defective components is at most . 10. The distributor decides to randomly select 10
components and to accept the batch only if the number of defective
components in the sample is at most 2.
a. What is the probability that the batch will be accepted when the
actual proportion of defectives is .01? .05? .10? .20? .25?
b. Let p denote the actual proportion of defectives in the batch. A
graph of P(batch is accepted) as a
horizontal axis and P(batch is accepted) on the vertical axis, is called the operating characteristic curve for the acceptance sampling plan. Use the results of part (a) to sketch this curve for 0≤p≤1.
c. Repeat parts (a) and (b) with "1" replacing "2" in the acceptance sampling plan.
d. Repeat parts (a) and (b) with "15" replacing "10" in the acceptance sampling plan.
e. Which of the three sampling plans, that of part (a), (c), or (d), appears most satisfactory, and why?
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