Suppose that two different tests A and B are to be given to a student chosen at random from a certain population. Suppose also that the mean score on test A is 85, and the standard deviation is 10; the mean score on test B is 90, and the standard deviation is 16; the scores on the two tests have a bivariate normal distribution; and the correlation of the two scores is 0.8.
a.) If the student scores an 80 on test A, what is the probability that her score on test B will be higher than 90?
b.) If a student is chosen at random what is the probability that the sum of her two scores from both tests will be greater than 200?