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 6000 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 company will accept __ of the shipments and will reject __ of the​ shipments

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Asked Oct 14, 2019
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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 6000 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 company will accept __ of the shipments and will reject __ of the​ shipments

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Expert Answer

Step 1

The probability that this whole shipment will be accepted is obtained below:

Here, the rates of defects is considered as a success, 5%, that is p = 0.05. The rates of not defects is considered as a failure, 95% (100% – 5%) of that is q = 0.95.

Therefore, the distribution is binomial distribution with sample size 52 and probability of success 0.05. That is, X~ Binomial (52, 0.05).

The formula for the probability of binomial distribution is,

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Р(х -х)-(Р)' (1- р)"" here x -0,1,2....,n for 0S ps1 -х

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Step 2

The required proba...

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P(X1) P(X 0) + P(X 1) 52 52 (0.05) 52-51 52 52-0 52 1 =0.06940.190 1 0.2598

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