A very large batch of components has arrived at a distributor. The batch can be
ID: 3150042 • Letter: A
Question
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective p components is at most.10. The distributor decides to randomly select 10 components and to accept the batch if the number of defective components in the sample is at most 2. What is the probability that the batch will be accepted if the actual proportion of defectives is.01 ?.05?.10?. 20?.25? Let p denote the actual proportion of defectives in the batch. A graph of P(batch is accepted) as a function of p (p is on the horizontal axis and P (...) on the vertical axis) is called the operating characteristic curve. Use the results of a) to sketch this curve fro 0 less than or equal to p less than or equal to 1. Repeats parts a) and b) with 1 replacing 2 in the acceptance sampling plan. Repeats parts a) and b) with 15 replacing 10 in the acceptance sampling plan. Which of the three sampling plans appears more satisfactory ?Explanation / Answer
a) Prob that batch is accepted = Prob (defectives <=2)
X no of defectives is binomial with n =10 and p varying.
p 0.01 0.05 0.1 0.2 0.25 Prob 0.9998 0.9885 0.9298 0.6778 0.5256