Question

Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 630 on the Verbal Reasoning section and 670 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 461 with a standard deviation of 107, and the mean score for the Quantitative Reasoning was 425 with a standard deviation of 154. 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 N( , )

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

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. She did the same on both sections
B. Quantitative Reasoning
C. Verbal Reasoning

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 54th54th percentile on the Quantitative Reasoning section? Round to the nearest integer.

10. What is the score of a student who scored worse than 94% of the test takers in the Verbal Reasoning section? Round to the nearest integer.

Answer 1

1. Verbal Reasoning section has a distribution N(461, 107)

Quantitative Reasoning section has a distribution of N(425, 154)

2. This is a normal distribution question with

= 630
P(x < 630.0)=?

z = 1.5794
3. This is a normal distribution question with

x = 670

z = 1.5909

4. Since their z score is greater for Quantitative Reasoning So B. Quantitative Reasoning