Probability value based on normal distribution.
Assume we draw two independent random samples, one consisting of 25 in-state first years and the other consisting of 25 out-of-state first years. What is the likelihood that the sample means score for in-state first years exceeds that of the out of state first years? Understand those two different tests, 1 and 2, are to be given to a student chosen at random from a certain population. Presume also 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 the standard deviation is 16; that the scores on the two tests have a bivariate normal distribution; and that the correlation of the two scores is 0.8. What is the probability that the sum of the student's scores on the two tests will be greater than 200?