When purchasing bulk orders of batteries, a toy manufacturer uses this acceptanc

Question

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 45 batteries and determine whether each is within specifications The entire shipment is accepted if at most 2 batteries do not meet specifications A shipment contains 6000 batteries, and 2% 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? The probability that this whole shipment will be accepted is (Round to four decimal places as needed) The company will accept % of the shipments and will reject Round to two decimal places as needed.) % of the shipments, so L

Explanation / Answer

Solution:-The probability that this whole shipment will be accepted is 0.9389.

For accepting shipment x < 2

P(Not meet specification) = 0.02

n = 45

x = 2

By applying binomial distribution:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 2) = 0.9389

The probability that this whole shipment will be accpeted is 0.9389.

For rejection we shoul have x > 2

x = 2

By applying binomial distribution:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 2) = 0.06101

The company will accept 93.89% of the shipments and will reject 6.10% of the shipments so almost all such shipments will be accepted.

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