The Graduate Record Examination (GRE) is a standardized test commonly taken by graduate school applicants in the United States. The total score is comprised of three components: Quantitative Reasoning, Verbal Reasoning, and Analytical Writing. The first two components are scored from 130 - 170. 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) A student scores 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. Relative to the scores of other students, which section did the student perform better on?

(b) Calculate the student's percentile scores for the two sections. What percent of test takers performed better on the Verbal Reasoning section?

(c) Compute the score of a student who scored in the \(80^{\text {th }}\) percentile on the Quantitative Reasoning section.

(d) Compute the score of a student who scored worse than \(70 \%\) of the test takers on the Verbal Reasoning section.