The mean score for freshmen on an aptitude test at a certain college is 540, with a standard deviation of 50. What is the probability that two groups of students selected at random, consisting of 32 and 50 students, respectively, will differ in their mean scores by
(a) More than 20 points?
(b) An amount between 5 and 10 points? Assume the means to be measured to any degree of accuracy.