Question

Let X represent the SAT score of an entering freshman at University X. The random variable X is shown to have a N(1200, 90) distribution. Let Y represent the SAT score of an entering freshman at University Y. The random variable Y is know to have N(1215, 110) distribution. A random sample of 100 freshman is obtained form each university. Let X bar = the sample mean of the 100 scores from university X and Y bar = the sample mean of the 100 scores from University Y. What is the probability that X bar will be greater than Y bar?