Consider again the two tests A and B described in Exercise 1. If a student is chosen at random and his score on test B is ] 00 what predicted value of his score on test A has the smallest M.S.E. and what is the value of this minimum M.S.E.?
Exercise 1
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; that the mean score on test B 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. If the student' s score on test A is 80, what is the probability that his score on test B will be higher than 90?