A professor wishes to make up a true-false exam with n questions. She assumes that she can design the problems in such a way that a student will answer the jth problem correctly with probability pj, and that the answers to the various problems may be considered independent experiments. Let Sn be the number of problems that a student will get correct. The professor wishes to choose pj so that E(Sn)=.7n and so that the variance of Sn is as large as possible. Show that, to achieve this, she should choose pj=.7 for all j; that is, she should make all the problems have the same difficulty.