A company uses the following acceptance-sampling procedure. A sample equal to 10% of the lot is taken. If 2% or less of the items in the sample are defective, the lot is accepted; otherwise, it is rejected. Submitted lots vary in size from 5,000 to 10,000 units.

a) Suppose that the lot size is = 5,000, what is the probability of accepting a given lot under this plan if the fraction defective in a lot is 2.5%?

b) Suppose that the lot size is = 10,000, what is the probability of accepting a given lot under this plan if the fraction defective in a lot is 2.5%?

c) In view of the answers in parts (a) and (b), what can you say about the protection of this plan?

d) If = 0.05 is the desired LTPD, does this scheme (i.e. acceptance-sampling plan) offer reasonable protection to the consumer? (Hint: Calculate the probability of accepting (or rejecting) lots for = 5,000 and = 10,000 when = 0.05 and comment on the results.)