question archive 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 ten syringes taken from the batch

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 ten syringes taken from the batch

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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 ten syringes taken from the batch. Suppose the batch contains 5% defective syringes.

(a)

Make a histogram showing the probabilities of r = 0, 1, 2, 3, ..., 9 and 10 defective syringes in a random sample of ten syringes. (Select the correct graph.)

(b)

Find μ (in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.)

μ = 2 syringes

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

3 syringes

(c)

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

4

(d)

Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

σ = 5 syringes

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Answer:

(a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, ..., 9 and 10 defective syringes in a random sample of ten syringes. (Select the correct graph.)

The correct graph is the third graph showing histogram probabilities of r = 0, 1, 2, 3, ..., 9 and 10.

(b) Find μ (in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.)

This is binomial distribution with n = 10 , p = 0.05

μ = np = 10 * 0.05 = 0.5

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

Expected number of defective defective syringes = 10 * 0.05 = 0.5

P( batch will be accepted) = p( x < 2 ) = p( x<=1)

= p( x = 0) + p( x = 1)

For binomial distribution,

p(x) = nCx px (1-p)n-x

Therefore,

p(x=0) + p(x=1) = 10C0 0.050 0.9510 +10C1 0.051 0.959

= 0.914

 

(d) Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

σ = Sqrt(np(1-p))

= sqrt(10*0.05*0.95)

= 0.689