A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 30 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 5% rate of defects, what is the probability that this whole shipment will be accepted?

Given that a pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 30 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications.

Probability for any random tablet to be defective is 0.05

Since 1000 s of tablets are there, we can assume that this p = 0.05 is constant for each draw and hence X no of defectives is binomial with n =30 and p =0.05

Prob that this whole shipment will be accepted

= P(X≤1)

=[tex]=30c0 (1-0.05)^{30} +30c1 (1-0.05)^{29}(0.05)\\=0.553542[/tex]