When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 49 b

Question

3 years ago

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When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 49 b

atteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 6000 batteries, and 1% 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?

Mathematics

1 answer:

Brilliant_brown [7] · Answer 1 · 2022-05-13T11:28:14+03:00

Answer:

Step-by-step explanation:

Given that A shipment contains 6000 batteries, and 1% of them do not meet specifications.

Sample size =49

If x is the number of batteries not meeting specifications then

x is binomial with n =49 and p = 0.01

Because i) each toy is independent of the other

ii) There are only two outcomes

Probability whole shipment is accepted = Prob (X≤3)

=0.9885

Hence almost all shipments would be accepted.

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 49 b

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 49 b