DCW Chemical is planning to implement an acceptance sampling plan for raw materi

Question

DCW Chemical is planning to implement an acceptance sampling plan for raw materials. A random sample of 22 batches from a large shipment (having a large number of batches) is selected. If two or more of the 22 batches fail to meet specifications, then the entire shipment is returned. Otherwise, the shipment is accepted.

In a sample of 22 batches from a population that is 1% defective (1% of the batches fail to meet specifications), find the probability that

a. two or more batches fail to meet specifications.
b. exactly two batches fail to meet specifications.
c. fewer than two batches fail to meet specifications

Explanation / Answer

PROBABILITY OF DEFECTIVE = 0.01

PROBABILITY OF NON DEFECTIVE = 0.99

A) P(TWO OR MORE ARE DEFECTIVE ) = 1 - [PROBABILITY 0 OR 1 ARE DEFECTIVE]

P(0) = 0.99^22 = 0.801

P(1) = 22C1*(0.01)^1*(0.99)^21 = 0.178

HENCE P(2 OR MORE ARE DEFECTIVE ) = 1 - 0.801 - 0.178 = 0.021

B)P(X=2 ARE DEFECTIVE ) = 22C2*(0.01)^2*(0.99)^20 = 0.018

C)P( LESS THEN 2 DEFECTIVE ) = P(0)+P(1) ( AS CALCULATED IN PART A) = 0.801+0.178 = 0.979

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