Homework Answers
(a)
Expected value of the number of defective items in the box = 100*Probability of defective =
= 100*(Probability that machine 1 produced defective + Probability that machine 2 produced defective + Probability that machine 3 produced defective)
Probability that machine 1 produced defective = Probability that box was produced by machine 1 * Probability of defective produced by machine 1 = 0.5*0.01 = 0.005
Probability that machine 2 produced defective = Probability that box was produced by machine 2 * Probability of defective produced by machine 2 = 0.3*0.02 = 0.006
Probability that machine 3 produced defective = Probability that box was produced by machine 3 * Probability of defective produced by machine 3 = 0.2*0.04 = 0.008
Probability of defective = 0.005 + 0.006 + 0.008 = 0.017
Expected value of the number of defective items in the box = 100*Probability of defective = 100*0.017 = 1.7
Varaince of the number of defective items in the box = 100*Probability of defective*(1-Probability of defective) =
= 100*0.017*(1-0.017) = 1.67
(b)
Probability that defective was produced by machine 1 = Probability that machine 1 produced defective / Probability of defective
= 0.005 / 0.017 = 0.294
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