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

Question

When purchasing bulk orders of? batteries, a toy manufacturer uses this acceptance sampling? plan: Randomly select and test 40 40 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 2 batteries do not meet specifications. A shipment contains 5000 5000 ?batteries, and 2 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?

Explanation / Answer

p =proportion of being defective or not meeting specification

here p = 0.02

X = number of items which does meet specification in 40 selected batteries

hen,x has binomial distribution with n=40,p=0.02

P(x=k)=40Ck*0.02k*0.9840-k

a)

P(shipment accepted)=P(x<=2)=P(x=0)+P(x=1)+P(x=2)

= 0.954397

95.44 % shipments will be accepted, 5.56% will be rejected.

So,most of the shipment will be accepted and very few will be rejected.

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