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2. A quality control inspection system requires that from each batch of items a sample of...

2. A quality control inspection system requires that from each batch of items a sample of 10 is selected and tested. If 2 or more of the sample are defective the whole batch is rejected.

If the probability of an item being defective is 0.05

(i.)What is the probability of 2 defectives in the sample? (6 points)

(ii.)What is the probability of the batch being rejected? (6 points)

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Answer #1

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AS FOR GIVEN DATA..

A quality control inspection system requires that from each batch of items a sample of 10 is selected and tested. If 2 or more of the sample are defective the whole batch is rejected.

If the probability of an item being defective is 0.05

Binomial Distribution PMF of B.D is f (k) (n k)pk (1-P)n-k Where k number of successes in trials n- is the number of independent trials p probability of success on each trial

(i.)What is the probability of 2 defectives in the sample? (6 points)

ANS::: probability of 2 defectives in the sample = (10c2)*(.05^2)*(.95^8) = .0746:  

(ii.)What is the probability of the batch being rejected? (6 points)

ANS ::  the probability of the batch being rejected = p(defectives >= 2) = 1- p(defectives = 0) - p(defective =1) = 1-.598 - 0.3151 = 0.0869

THANK YOU.....!!!!

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