In a study of graduate students who took the Graduate Record Exam (GRE), the Educational Testing Service recently reported that for the quantitative exam, U.S.

citizens had a mean of 529 and standard deviation of 127, whereas the non-U.S. citizens had a mean of 649 and standard deviation of 129.

(a) Both groups had about the same amount of variability in their scores, but non-U.S. citizens performed better, on the average, than U.S. citizens.

(b) If the distribution of scores was approximately bell shaped, then almost no U.S. citizens scored below 400.

(c) If the scores range between 200 and 800, then probably the scores for non-U.S. citizens were symmetric and bell shaped.

(d) A non-U.S. citizen who scored three standard deviations below the mean had a score of 200.