The quality control inspector o a production plant will re ect a batch o syringe

Question

The quality control inspector o a production plant will re ect a batch o syringes if two or more detective syringes are found in a random sample o eleven syringes taken from the batch. Suppose the batch contains 1% defective syringes (a) Make a histogram showing the probabilitles ofr 0, 1, 2, 3, 10 and 11 defective syringes in a random sample of eleven syringes. 0.5 035 03 025 0 15 012 34587 9 10 1 23456891011 0.3 08 0.25 0.6 02 0.05 0 1 23456789 10 1 0 1 2345678 9 10 11 (b) Find (Enter your answer to two decimal places.) What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.) (c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.) (d) Find (Roun d your answer to three decimal p aces.)

Explanation / Answer

a) Histogram = D option

b) = 11 * 0.01 = 0.11

Expected syringes = 0.11

c)  P(X<2) = 1 - P(X=0) - P(X=1)

P(X<2) = 1 - (11C0 * 0.01^0 0.99^11) - (11C1 * 0.01^1 0.99^10)

P(X<2) = 1 - 0.8953 - 0.0995

P(X<2) = 0.005

d) = n*p*(1-p)

= 11 * 0.01 * 0.99 = 0.109

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