Suppose a writer is working on a book and the number of pages that he writes each day is modeled by a random variable X, where Ex(X) = 20.

(a) What is the upper bound on the probability that he writes at least 50 pages on a given day?

(b) Let Var(X) = 10. Provide a tighter upper bound than (a) on the same probability that he writes at least 50 pages.

(c) Use Chebyshev's inequality to give a lower bound on Pr(15 < X < 25), still assuming Ex(X) = 20 and Var(X) = 10.