Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 610 on the Verbal Reasoning section and 660 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 459 with a standard deviation of 113, and the mean score for the Quantitative Reasoning was 447 with a standard deviation of 155. Suppose that both distributions are nearly normal. A) Write down the short-hand for these two normal distributions.
B) What is her Z score on the Verbal Reasoning section?
C) What do these Z scores tell you?
D) Relative to others, which section did she do better on?
E) Find her percentile scores for the two exams.
F) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?
G) Explain why simply comparing her raw scores from the two sections would lead to the incorrect conclusion that she did better on the Quantitative Reasoning section.
H) If the distributions of the scores on these exams are not nearly normal, would your answers to parts (b) - (f) change? Explain.