Question

(13 points) Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 620 on the Verbal Reasoning section and 750 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 467 with a standard deviation of 109, and the mean score for the Quantitative Reasoning was 441 with a standard deviation of 155. Suppose that both distributions are nearly normal. Round calculated answers to 4 decimal places unless directed otherwise. 1. Write down the short-hand for these two normal distributions. The Verbal Reasoning section has a distribution NC The Quantitative Reasoning section has a distribution of NC 2. What is her Z score on the Verbal Reasoning section? 3. What is her Z score on the Quantitative Reasoning section? 4. Relative to others, which section did she do better on? A. Quantitative Reasoning B. Verbal Reasoning C. She did the same on both sections 5. What is her percentile score on the Verbal Reasoning section? Round to nearest whole number. 6. What is her percentile score on the Quantitative Reasoning section? Round to nearest whole number. 7. What percent of the test takers did better than she did on the Verbal Reasoning section? 8. What percent of the test takers did better than she did on the Quantitative Reasoning section? 9. What is the score of a student who scored in the 73th percentile on the Quantitative Reasoning section? Round to the nearest integer. 10. What is the score of a student who scored worse than 37% of the test takers in the Verbal Reasoning section? Round to the nearest integer.

Answer 1

Ans:

1)The Verbal Reasoning section has a distribution N(467 ,109 )

The Quantitative Reasoning section has a distribution of N(441 , 155)

2)Z score on the Verbal Reasoning section=(620-467)/109=1.4037

3)Z score on the Quantitative Reasoning section=(750-441)/155=1.9935

4)Quantitative reasoning,as z score is higher

5)percentile score on the Verbal Reasoning section=100*P(z<=1.4037)=92

6)percentile score on the Quantitative Reasoning section=100*P(z<=1.9935)=98

7)percent of the test takers did better than she did on the Verbal Reasoning section=8%

8)percent of the test takers did better than she did on the Quantitative Reasoning section=2%

9)P₇₃=norminv(0.73,441,155)=536

10)If he score worse than 37% of the test takers,than 63% scored worse than him.

P₆₃=norminv(0.63,467,109)=503