A company makes hydraulic cylinders.A final quality check determines whether or

Question

A company makes hydraulic cylinders.A final quality check determines whether or not a production lot meets standards and may be shipped to customers.Historically,20 percent of the cylinders manufactured have not met standards.A sample of 15 cylinders is tested.

a)what is the expected number of defective cylinders in the sample?

b)if two less bad cylinders are discovered in the sample,the lot is assumed to be good.what is the probabiity that the lot is good?

c)what is the probability of exactly two defectives if the percent defective is now 6%?set up formula.Do not solve.

Explanation / Answer

20 percent of the cylinders manufactured have not met standards.

probability of defective = p = 0.20, n = 15

a) E(x) = n*p=15*0.20 = 3

b) If two less bad cylinders are discovered in the sample,the lot is assumed to be good. So probability that the lot good is given by,

p ( x < 2) = p ( x = 0 ) + p ( x = 1 )

p ( x = 0 ) = nCx * px * (1-p)n-x

               = 15C0 * 0.200 * (1-0.20)15-0

                   = 0.0352

p(x = 1 ) = 15C1 * 0.201 * (1-0.20)15-1

             = 0.1319

p ( x < 2 ) = 0.0352 + 0.1319 = 0.1671

c) Here the percent defective is now 6%.

p = 0.06

p ( x = 2 ) = nCx * px * (1-p)n-x

               = 15C2 * 0.062 * (1-0.06)15-2

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