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?

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19-02-2018
Mathematics

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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?

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MsEHolt MsEHolt · Answer 1 · 2018-03-01T03:58:04+01:00

We use the binomial distribution:
[tex]P _{a}= \sum^c_d_=_0 \frac{n!}{d!(n-d)!} p^d (1-p)^n^-^d[/tex]
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.