Question

I need 5~10 please! thank you

Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 510 on the Verbal Reasoning section and 650 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 470 with a standard deviation of 127, and the mean score for the Quantitative Reasoning was 429 with a standard deviation of 153. 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(470, 127 )

The Quantitative Reasoning section has a distribution of N (429,153)

2. What is her Z score on the Verbal Reasoning section? 0.3149

3. What is her Z score on the Quantitative Reasoning section? 1.4444

4. Relative to others, which section did she do better on?

A. Quantitative 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 41th percentile on the Quantitative Reasoning section? Round to the nearest integer.

10. What is the score of a student who scored worse than 92% of the test takers in the Verbal Reasoning section? Round to the nearest integer.

Answer 1

5) By percentile score we mean the position of the score in the values arranged in some order. For eg median is the middle most observation in any arranged series. So its percentile score is always 50%. Similarly percentile score of 510 among the verbal reasoning section is obtained from the normal table by looking at the percentage of observations lying below 510 among the verbal reasoning scores. This is obtained by finding out the area to the left of 0.3149(z score of 510) from the standard normal table, which is around 62%.

6) Similarly percentile score for 650 can also be calculated with the help of its z score 1.444, which is around 93% so we can say the 93rd percentile is 650.

7) The percent of test takers who did better than she did on verbal reasoning is the area on the standard normal curve towards the right side of the z score. Around 38% of the scores are above 510 in this section

8) Around 7.44% of the scores in Quantitative reasoning section are above 650

9)The z score corresponds to the probability 0.41 in the standard normal curve is -.2275. The required score can be obtained by multiplying the z score with standard deviation and adding the mean score. ie Score of the student who scored 41th percentile is -0.2275*153+429

10) Let X be the score of the student such that 92% of the test takers have score above X. The area to the right of z score -1.405 is 0.92 .Now to find X this z score has to be multiplied with  standard deviation and adding the mean score. ie -1.405*127+470= score of the student who scored worse than 92% of the test takers in the verbal reasoning section