In a shipment of 60 cars to automobile dealers in the Town of Richvale, 15 had defective radios installed. Let us define X as the number of defective radios installed. (a) (i) What is the probability that in a sample of ten automobiles inspected, more than three had defective radios installed? (ii) What is the probability that in a sample of ten automobiles inspected, more than 2 but no more than 4, had defective radios installed? (b) What are the mean and variance of defective radios installed you would expect if you sampled twenty automobiles? (c) Recall that X was defined as the number of defective radios installed. Based on your part (b) solution, what is the value of E(3X + 6) + V(4X+ 8)?

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