Question

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 35 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 4000 ​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

Here we have

Let X is a random variable shows the number of batteries do not meet specifications in the sample. Since population is very large from sample size, that is so we can use binomial distribution. That is X has binomial distribution with parameters n=35 and p=0.02.

The probability that shipment will be accepted is:

Answer: 0.9949

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That is the company will accept 99.49% of the shipments and will reject 0.51% of the shipment so almost all of the shipments will be accepted.