Question

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 37 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 ​batteries, and 2​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

Answer 1

The probability that the whole shipment is accepted is computed here as:

= Probability that there are 0, 1, 2 or 3 defective ones in the 37 selected from 3000 batteries

Total defective ones from 3000 batteries is computed here as:
= 0.02*3000 = 60

Therefore, the probability here is computed as:

Therefore 0.9942 is the required probability here.

As the probability here is more than 0.99, therefore almost all such shipments would be accepted.