Magnetron tubes are produced on an automated assembly

Chapter , Problem 2.26

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Magnetron tubes are produced on an automated assembly line. A sampling plan is used periodically to assess quality of the lengths of the tubes. This measurement is subject to uncertainty. It is thought that the probability that a random tube meets length specification is 0.99. A sampling plan is used in which the lengths of 5 random tubes are measured. (a) Show that the probability function of Y , the number out of 5 that meet length specification, is given by the following discrete probability function: f(y) = 5! y!(5 y)!(0.99)y(0.01)5y, for y = 0, 1, 2, 3, 4, 5. (b) Suppose random selections are made off the lineand 3 are outside specifications. Use f(y) above either to support or to refute the conjecture that the probability is 0.99 that a single tube meets specifications.