The quality-control inspector of a production plant will reject a batch of syrin

Question

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of seven syringes taken from the batch. Suppose the batch contains 1% defective syringes.

(a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, ..., 6 and 7 defective syringes in a random sample of seven syringes.

(b) Find . (Enter your answer to two decimal places.)
=  syringes

What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.)
syringes

(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)


(d) Find . (Round your answer to three decimal places.)
=  syringes

Explanation / Answer

a) bottom right curve is right

b) mean =np =7*0.01 =0.07

c) expected number of defective syringes the inspector will find =0.07

d) probability that the batch will be accepted =P(X<=1) =P(X=0)+P(X=1)=0.932+0.066 =0.998

d) =(np*(1-p))1/2 =0.263

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