Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 58 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 3% 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?

a. The probability that this whole shipment will be accepted is ?

b. The company will accept ___% of the shipments and will reject ___% of the shipments.

Answer #1

Binomial distribution: P(X) = nCx p^{x}
q^{n-x}

Sample size, n = 58

P(a tablet not meeting specification), p = 0.03

q = 1 - p = 0.97

P( whole shipment will be accepted) = P(0 or 1 not meeting specification)

= P(0) + P(1)

= 0.97^{58} + 58x0.03x0.97^{57}

= 0.1709 + 0.3066

= 0.4775

a. The probability that this whole shipment will be accepted is
**0.4775**

b. a. The probability that this whole shipment will not be accepted = 1 - 0.4775

= 0.5225

The company will accept **47.75**% of the
shipments and will reject **52.25**% of the
shipments

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