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Q1) Assumer we draw 2 independent random samples, one consisting of 25 in-state first years and other consisting of 25 out-of-state first years. Determine the probability that sample mean score for in-state first years exceeds that of out of state first years? Assume that 2 different tests, 1 and 2, are to be given to student selected at random from certain population. Assume also that mean score on test 1 is 85 and standard deviation is 10; that mean score on test 2 is 90 and standard deviation is 16; that scores on two tests have a bivariate normal distribution; and that correlation of 2 scores is 0.8. Determine the probability that sum of the student's scores on 2 tests will be greater than 200?

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