A manufacturer of metal piston finds that on the average 12% of his pistons are

Question

A manufacturer of metal piston finds that on the average 12% of his pistons are rejected because they are either oversized or undersized what is the probability that a batch of 10 pistons will contain 1) no more than 2 reject 2) at least two rejects ? A manufacturer of metal piston finds that on the average 12% of his pistons are rejected because they are either oversized or undersized what is the probability that a batch of 10 pistons will contain 1) no more than 2 reject 2) at least two rejects ? 1) no more than 2 reject 2) at least two rejects ?

Explanation / Answer

P(rejection), p = 0.12

q = 1 - 0.12 = 0.88

n = 10

1) P(no more than 2 are rejected) = P(0) + P(1) + P(2)

= 0.8810 + 10x0.12x0.889 + 10C2x0.122x0.888

= 0.2785 + 0.3798 + 0.2330

= 0.8913

2) P(at least two are rejected) = 1 - P( less than 2 rejected)

= 1 - P(0) - P(1)

= 1 - 0.2785 - 0.3798

= 0.3417

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