A college is considering new core curriculm that would need all undergraduates to study foreign language. The student newspaper plans to interview several faculty members and report thier opinions. Assume that in fact 60% of faculty support the language requirement.
a) If the newspaper interviews five faculty members, determine the probability that a majority (that is 3 or more) oppose the language requirement? (suppose that the faculty members are chosen at random)
b) If 15 faculty are interviewed instead, determine the probability that a majority (8 or more) oppose the requirement? Larger samples make it less likely that majority opinion in the population is incorrectly reported.