Stats Homework question

Question

Sophia who took the Graduate Record Examination (GRE) scored 168 on the Verbal Reasoning section and 153 on the Quantitative Reasoning section. Suppose mean score for Verbal Reasoning section for all test takers was 154 with a standard deviation of 7.25, and the mean score for the Quantitative Reasoning was 151 with a standard deviation of 7.3. Suppose that both distributions are nearly normal.

What is Sophia's Z-score on the Verbal Reasoning section?



On the Quantitative Reasoning section?



What was her percentile score on the Verbal Reasoning section?


What was her percentile score on the Quantitative Reasoning section?

Answer 1

Hi Adrian,

 

Any z score can be found with the equation z = (X - M)/SD where X is a person's score, M is the mean and SD is the standard deviation.

In your example, the z score for verbal is (168 - 154)/7.25 = 1.931. For quantitative, it is (153 - 151)/7.3 = 0.274.

 

The percentile for each of these scores is the percentage of people who score at or below that score (e.g. the percentage of people who score 168 or below on the verbal test). To find these values, your teacher should have given you a normal distribution table. If not, they can be found online.

For verbal, she is in the 97.3 percentile.

For quantitative, she is in the 60.8 percentile.

 

Hope that helps.