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

Question

Mathematics

Emily House

23 September, 13:18

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

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Answers (1)

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Ella Gardner · Answer 1

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.