Let Sn be the number of successes in n independent trials. Use the program BinomialProbabilities (Section 3.2) to compute, for given n, p, and j, the probability

P (−j√npq < Sn − np < j√npq) .

(a) Let p = .5, and compute this probability for j = 1, 2, 3 and n = 10, 30, 50. Do the same for p = .2.
(b) Show that the standardized random variable S*n = (Sn − np)/√npq has expected value 0 and variance 1. What do your results from (a) tell you about this standardized quantity S+n?