A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 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?

Question

contestada

Respuesta :

windyyork windyyork · Answer 1 · 2019-07-09T09:22:25+02:00

Answer: Hence, the probability that the whole shipment would be accepted is 0.371.

Many would be rejected.

Step-by-step explanation:

Since we have given that

Number of tablets to be tested = 42

Probability of getting a defect = 5% = 0.05

We need to find the probability that this whole shipment will be accepted.

As we have mentioned that if there is only one or none defect, then the whole shipment would be accepted.

P(accepted) = P(either none or one defect) = P(X=0)+P(X=1)

[tex]P(X=0)=(1-0.05)^{42}=(0.95)^{42}=0.115\\\\and\\\\P(X=1)=42\times (0.05)(0.95)^{41}=0.006\times 42=0.256[/tex]

So, P(Accepted) = 0.115+0.256=0.371

Hence, the probability that the whole shipment would be accepted is 0.371.

Many would be rejected.