4 Navidi, Statistics or Engineers and Scientists, 3rd Edition, p.213, Exercise #

Question

4 Navidi, Statistics or Engineers and Scientists, 3rd Edition, p.213, Exercise #13)Ofthe items manufactured fora certain application, 90% meet the length specification and can be used immediately. Suppose that a random sample of 10 such bolts is selected. (a-3 pts.) Let Y the number of items in the sample that can be used immediastely. Identify the distribution of the random variable Y. Specify the value(s) of all relevant parameter(s) (b-5 pts.) Find the probability that at least 9 of the items in the sample can be used immediately.

Explanation / Answer

a) This is binomial distributuion.

n = 10 and p = 0.9

P(X = x) = 10Cx * 0.9x * (1 - 0.9)10-x

b) P(X > 9) = P(X = 9) + P(X = 10)

                  = 10C9 * 0.99 * 0.11 + 10C10 * 0.910 * 0.10

                  = 0.7361

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