7.9k views
5 votes
When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: randomly select and test 5858 batteries and determine whether each is within specifications. the entire shipment is accepted if at most 22 batteries do not meet specifications. a shipment contains 70007000 ​batteries, and 11​% 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?

User Speigg
by
7.7k points

1 Answer

3 votes
We use the binomial distribution:

P _(a)= \sum^c_d_=_0 (n!)/(d!(n-d)!) p^d (1-p)^n^-^d
In this formula, c is the acceptable number of defectives; n is the sample size; p is the fraction of defectives in the population. Our c is 2; n is 58; and p is 0.11. Once we evaluate that summation, we get 0.0388. This has a 3.88% chance of being accepted. Since this is such a low chance, we can expect many of the shipments like this to be rejected.
User Mario David
by
9.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories