The mean score for freshmen on an aptitude test at a certain college is 570, with a standard deviation of 40. Assume the means to be measured to any degree of accuracy. What is the probability that two groups selected at random, consisting of 54 and 40 students, respectively, will differ in their mean scores by-
(a) more than 13 points?
(b) an amount between 2 and 7 points?