A pharmaceutical company receives large shipments of aspirin tablets. The accept

Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 52 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 7000 aspirin tablets actually has a 5%

rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

The probability that this whole shipment will be accepted is

.

(Round to four decimal places as needed.)

The company will accept % of the shipments and will reject % of the shipments, so many of the shipments will be rejected.

(Round to two decimal places as needed.)

Explanation / Answer

Probability that whole shipment will be accepted = P(x=0 or 1)

p=probability of defect=0.05

Probability = 52C0 * 0.95^52+ 52C1* 0.05*0.95^51=0.95^52+ 52*0.05*0.95^51= 0.2594

Company will accept 25.94% of all shipments and reject 74.06% of all shipments.

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