A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 47 ​tablet

Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 47 ​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 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?

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Josephine 5 days 2021-10-08T09:36:15+00:00 1 Answer 0

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    2021-10-08T09:38:00+00:00

    Answer:

    The probability that the whole shipment will be​ accepted is 0.5862.

    Step-by-step explanation:

    Let X = number of the aspirin tablets that doesn’t meet the required specifications.

    The probability of the random variable X is, P (X) = p = 0.03.

    The sample of n = 47 tablets are tested from each batch.

    The probability of any of the tablets being defective is independent of the others.

    The probability mass function of X is,

    P(X=x)={n\choose x}p^{x}(1-)^{n-x};\ x=0,1,2,3...

    Compute the probability that the whole shipment of 3000 tablets will be​ accepted as follows:

    P (X ≤ 1) = P (X = 0) + P (X = 1)

                 ={47\choose 0}0.03^{0}(1-0.03)^{47-0}+{47\choose 1}0.03^{1}(1-0.03)^{47-1}\\=0.2389+0.3473\\=0.5862

    Thus, the probability that the whole shipment will be​ accepted is 0.5862.

    The sample of 47 tablets is significantly small when drawn from a population of 3000 tablets. So it is difficult to make conclusion about all such shipments of aspirin tablets.

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