Question

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A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 59 tablets, then accept the whole batch if there is
only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 2% 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.)
4

Answer 1

• The probability that this whole shipment will be accepted is 72.39%.

Explanation:

The probability of no defects with 2% rate of defects:

• P(no defects) = 59*0.02⁰*(1 - 0.02)⁵⁹ = 0.3583 (rounded) = 35.83%

Probability of exactly one defect:

• P(1 defect) = 59*0.02¹*(1 - 0.02)⁵⁸ = 0.3656 (rounded) = 36.56%

Probability of one or no defects:

• P(1 or none) = 35.83% + 36.56% = 72.39%

This indicates that:

• 100% - 72.39% = 27.61% of shipments will be rejected, it is a lot, so many shipments will be rejected

The probability that this whole shipment will be accepted is 72.39%.