(a) The number of automobiles sold weekly at a certain dealership is a random variable with expected value 16. (i) Give an upper bound to the probability that next week's sales exceed 18. (ii) Suppose now that the variance of the number of automobiles sold weekly is 9. Give a lower bound to the probability that next week's sales are between 10 and 22, inclusively. (b) If E[X] = 75, E[Y] = 75, Var-(X) = 10, Vor") = 12 and Cov[X,Y) = 3, give an upper bound for P[|X YI :5 15). (c) Of a collection of 4D batteries, each battery is equally likely to be either a type A or a type B battery. Type A batteries last for an amount of time that has mean 50 and standard deviation 15. Type B batteries last for an amount of time that has mean 30 and standard deviation 6. Derive an expression, in terms of the CDF of a standard normal random variable, for the probability that the total life of all 40 batteries exceeds 1700