# Please answer me this question A manufacturer considers a production lot unacceptable if 10% or more of the units in the lot are defective. In such cases the company wants to scrap the entire lot. A company quality control inspector has proposed the following criterion for determining whether to reject a lot; In a sample of 10 units from a lot, if two or more are defective, reject the entire lot. If the lot currently under examination is 11% defective, what is the probability that this decision rule will lead the quality control inspector to the correct decision?

The manufacturer rejects the lot if 10% or more of the units are defective.

In the lot being considered 11% of units are defective and it should be rejected.

Using the quality control inspector's criterion, 10 units are chosen from the lot and if 2 or more are defective the lot is rejected. When 10 units are chosen from the lot under consideration there 10*0.11 = 1.1 defective units; as the number of defective units has to be a whole number there are 2 defective units. When 2 units are chosen from this lot, the probability that both the units chosen are defective is (2/10)*(1/9) = 1/45

The probability that the correct decision is taken in this case using the quality control inspector's method is 1/45 = 0.022.

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