Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 19 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3​% rate of​ defects, what is the probability that this whole shipment will be​ accepted?

Answer 1

Probability will be 0.5779

Explanation:

Number of tablets n = 19

Probability of defect rems that is p = 0.03

Here number of trials is fixed and probability of success = 0.03

Here p = 0.03

So q = 1 - p = 1 -0.03 = 0.97

By using binomial distribution

Probability is given by
`^nC_rp^rq^(n-r)`

So P(0 or 1) =
`^(19)C_0{0.03}^0{0.97}^(19-0)+^(19)C_1{0.03}^1{0.97}^(19-1)=0.5606+0.0173=0.5779`