LE 12 - Normal Distribution Applications OPEN Sophia who took the Graduate Record Examination (GRE) scored 168 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 150 with a standard deviation of 7, and the mea score for the Quantitative Reasoning was 150 with a standard deviation of 7.29. Suppose that both distributions are nearly normal. (a) What is Sophias Z-score on the Verbal Reasoning section? 2.57143 On the Quantitative Reasoning section? 0.960219 (b) Relative to others, which section did she do better on? Did better on Verbal (c) Find her percentile scores for the two exams. Verbal Reasoning percentile: 49.49 Quantitative Reasoning percentile: 33.15 th th (d) What percent of the test takers did better than her on the Verbal Reasoning section? (Enter the percent sign with your answer.) 50.51% On the Quantitative Reasoning section? 66.85% Find the following: (e) The score of a student who scored in the 25th percentile on the Quantitative Reasoning section. 145.28 (f) The score of a student who scored worse than 75% of the test takers in the Verbal Reasoning section. 146.5