A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 39 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 4000 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?

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MrRoyal MrRoyal · Answer 1 · 2022-03-02T11:03:23+01:00

Probabilities are used to determine the chances of a shipment being accepted or rejected

The rate of defect is 5%.

So, the probability that a tablet is not defect is 95%

The probability that there is no defect out of the 39 selected tablets is:

[tex]P(None) = 0.95^{39}[/tex]

[tex]P(None) = 0.1352[/tex]

The probability that there is one defect out of the 39 selected tablets is:

[tex]P(One) = 39 * 0.05 * 0.95^{38}[/tex]

[tex]P(One) = 0.2777[/tex]

Add both probabilities

[tex]P(Accepted) = 0.1352 + 0.2777[/tex]

[tex]P(Accepted) = 0.4129[/tex]

Hence, the probability that a shipment will be accepted is 0.4129

The above probability is less than 0.5.

This means that many shipments will be rejected