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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?

Respuesta :

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.

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