Records of a university (collected over many years) show that on the average 74 percent of all incoming freshmen have I.Q.’s of at least 115. Of course, the percentage varies somewhat from year to year, and this variation is measured by a standard deviation of 3 percent. If a sample check of 30 freshmen entering the university in 2003 showed that only 18 of them have I.Q.’s of at least 115, estimate the true proportion of students with I. Q.’ s of at least 115 in that freshman class using
(a) Only the prior information;
(b) Only the direct information;
(c) The result of Exercise 10.74 to combine the prior information with the direct information.