A machine shop orders 200 bolts from a supplier. To determine whether to accept

Question

A machine shop orders 200 bolts from a supplier. To determine whether to accept the shipment of bolts, the manager of the facility randomly selects 30 bolts without replacement. If of the 30 randomly selected bolts 2 or less are found to be defective, he concludes that the shipment is acceptable i. If 20% of the bolts in the population are defective, what is the probability that the shipment is acceptable? ii. Now assume the 30 bolts are chosen with replacement. If 20% of the bolts in the population are defective, what is the probability that the shipment is acceptable?

Explanation / Answer

Number of defective bolts = 200x0.2 = 40

i) P(shipment is acceptable) = P(0 defective) + P(1 defective) + P(2 defective)

= 160C30/200C30 + 160C29x40C1/200C30 + 160C28x40C2/200C30

= 0.0007 + 0.0061 + 0.0263

= 0.0331

ii) P(shipment is acceptable) = P(0) + P(1) + P(2)

= 0.830 + 30C1x0.2x0.829 + 30C2 x 0.22 x 0.828

= 0.0012 + 0.0093 + 0.0337

= 0.0442

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