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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?