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23 April, 21:09

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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  1. 23 April, 23:40
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    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.
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