Question

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?

Answer 1

Explanation:

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)

=
`=30c0 (1-0.05)^(30) +30c1 (1-0.05)^(29)(0.05)\\=0.553542`