Magnetron tubes are produced from an automated assembly line. A sampling plan is used periodically to assess quality on 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(b) Suppose random selections arc made off the line and 3 are outside specifications. Use f(v) above either to support or refute the conjecture that the probability is 0.99 that a single tube meetsspecifications.

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5! (0.99) (0.01)-, f(y) = y!(5 – y)!