Question

Suppose that on a certain examination in advanced mathematics, students from University A achieve scores which are normally distributed with a mean of 625 and a variance of 100, and that students from University B achieve scores which are normally distributed with a mean of 600 and a variance of 150. If two students from university A and three students from university B take this examination, what is the probability that the average of the scores of the two students from university A will be greater than average of the scores of the three students from University B? Suggestion: Find the distribution of the difference between the two averages.