(3) A company produces microchips and supplies them to a distributor of electron

Question

(3) A company produces microchips and supplies them to a distributor of electronic equipment. The microchips are supplied in batches of 200. The distributor regards a batch as acceptable if 10 or fewer of the chips are defective (the distributor knows that it’s impossible to always produce non-defective chips). Rather than test all 200 chips in a batch, the distributor randomly selects a sample of 20 chips from each batch and tests them. The distributor assumes that if 2 or more of the chips in the sample are defective, then the batch is not acceptable and the batch will be rejected. Otherwise the batch is accepted.

(a) Suppose that in a given batch of 200 chips, 15 are defective. What is the probability that the distributor finds this batch acceptable?

Explanation / Answer

P(defective) = 15/200 = 0.075

P(finds batch acceptable) = P(20 acceptable) + P(19 acceptable)

= (1-0.075)20 + 20x(1-0.075)19x0.075

= 0.5513

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