A leather bag manufacturing company supplies bags in lots of size 200 to a buyer. A sample of 2 begs is drawn and the corresponding lot is accepted if and only if both begs are nondefective. The company and the buyer decide that AQL = 0.04 and LTDD = 0.10. If there are 15 defective bags in each lot, compute the

(i) Probability of accepting the lot,

(ii) Producer’s risk and consumer’s risk,

(iii) AOQ, if the rejected lots are screened and all defective bags are replaced by nondefectives, and

(iv) Average total inspection.

To solve this problem using probability theory, we'll need to apply the concepts of Acceptance Quality Level (AQL), Lot Tolerance Percent Defective (LTDD), Producer's Risk, Consumer's Risk, Average Outgoing Quality (AOQ), and Average Total Inspection. Let's address each part of the question step by step:

(i) Probability of accepting the lot:
AQL is the maximum acceptable percentage of defective items in a lot. AQL = 0.04, which means that the buyer is willing to accept a lot if it has no more than 4% defective bags. The lot contains 15 defective bags out of 200, so the probability of accepting the lot is the probability that both bags drawn are non-defective.

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