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Test mean aptitude test scores of two groups of freshman students

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The mean score for freshman on an aptitude test at a certain college is 800 with a standard deviation of 50. That is the probability that two groups of students selected at random, consisting of 36 and 49 students, respectively, will differ in their mean scores by: (Assume mean scores are continuous)

a) more than 12 points?

b) an amount between 7 and 15 points?

The professor listed the answers to be:
a) 13.7%
b) 17.6%

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