This Test: 100 pls possible When purchasing bulk orders of batteries, a toy manu

Question

This Test: 100 pls possible When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specificati s 5 00 bater es, and 2% ofthem 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? A shipment contains 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 7% of the shipments so I Round to two decimal places as needed) Enter your answer in each of the answer boxes Welcome to MyStatLab 0

Explanation / Answer

shipment will be accepted if at most 2 batteries doesnt meet expectation

so that means we have to find P(at most 2) =P(x<= 2)

we use binomial distribtion formula

P=nCr p^r q^(n-r)

n=55

p=2% =0.02

q=1-p =1-0.02 =0.98

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

               =55C0 (0.02)^0 (0.98)^55 + 55C1 (0.02)^1 (0.98)^54 + 55C2 (0.02)^2 (0.98)^53

               =0.32918 + 0.36948836 + 0.2035956

               =0.9023

b)

The company will accept 90.23% of the shipments and will reject 9.77% of he shipments,so it will accept almost all the shipments

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