19. George got 70% on an economics exam where the mean was 55% and the variance was 9. If a professor wishes to change the distribution of marks so that they have a mean of 70% and a standard deviation of 5, what will George’s new mark be?
a) 95%
b) 85%
c) 90%
d) Over 100%
The answer is A, but don't know why
If the original variance is 9 than the standard deviation is 3. George's score of 70 is 5 standard deviations from the mean (70-55=15/3=5).
Then if the mean is moved to 70 we need to add 5 standard deviations to is (5 x 5 = 25) so his new score is 95.