The quality control inspector of a production plant willreject a batch of syring

Question

The quality control inspector of a production plant willreject a batch of syringes if two or more defective syringes arefound in a random sample of eight 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, 4, 5, 6, 7, or 8 defective syringes in a random sample of eightsyringes. b. Find . What is the expected number of defectivesyringes the inspector will find? c. What is the probability that the batch will beaccepted? d. Find . The quality control inspector of a production plant willreject a batch of syringes if two or more defective syringes arefound in a random sample of eight 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, 4, 5, 6, 7, or 8 defective syringes in a random sample of eightsyringes. b. Find . What is the expected number of defectivesyringes the inspector will find? c. What is the probability that the batch will beaccepted? d. Find .

Explanation / Answer

For (a), usehttp://www.stat.tamu.edu/~west/applets/binomialdemo.html togenerate the histogram Let X be the number of defectve syringes X~(n = 8, p = 0.01) (b) = np = 8 x 0.01 = 0.08 (expected number = 1) (c) P(the batch will be accepted) = P(less than 2 defectivesyringes) = P(X = 0) + P(X = 1) = 0.9973 (d) = (npq) = (8 x 0.01 x 0.99) = 0.2814 Hope this helps!

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