4.3 GRE scores, Part I: Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.
a) What was Sophia's z-score on the Verbal Reasoning section?
(please round to two decimal places)
b) What was Sophia's z-score on the Quantitative Reasoning section?
(please round to two decimal places)
c) On which of the two exams did she do relatively better?
d) What percentage of test takers did she do better than on the Verbal Reasoning section?
% (please round to two decimal places)
e) What percentage of test takers did she do better than on the Quantitative Reasoning section?
% (please round to two decimal places)