Professor A and Professor B are teaching sections of the same introductory statistics course and decide to give common exams. They both have 25 students and design the exams to produce a grade distribution that follows a bell curve with mean μ = 75 and standard deviation σ = 10.
(a) Suppose students are randomly assigned to the two classes and the instructors are equally effective. Describe the center, spread, and shape of the distribution of the difference in class means, x̅_A − x̅_B, for the common exams.
(b) Based on the distribution in part (a), how often should one of the class means differ from the other class by three or more points?
(c) How do the answers to parts (a) and (b) change if the exams are much harder than expected so the distribution for each class is N(60, 10) rather that N(75, 10)?