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Assume we draw two independent random samples, one comprising of 25 in-state first years and other consisting of 25 out-of-state first years. What is the probability that the sample mean score for in-state first yearsexceeds that of out of state first years? Assume that two different tests, 1 and 2, are to be given to the student selected at random from the certain population. Assume as well that the mean score on test 1 is 85 and the standard deviation is 10; that the mean score on test 2 is 90 and standard deviation is 16; that the scores on the two tests have the bivariate normal distribution; and that the correlation of two scores is 0.8. What is the probability that the sum of student's scores on the two tests will be greater than 200?

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