Question

1. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section
and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all
test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning
was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.
a. Write down the short-hand for these two normal distributions.
b. What is Sophia’s Z-score on the Verbal Reasoning section? On the Quantitative Reasoning
section? Draw a standard normal distribution curve and mark these two Z-scores.
c. What do these Z-scores tell you?
d. Relative to others, which section did she do better on?
e. Find her percentile scores for the two exams.
f. What percent of the test takers did better than her on the Verbal Reasoning section? On the
Quantitative Reasoning section?

Answer 1

Given :  Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section  and 157 on the Quantitative Reasoning section.

To Find :   Z score  and percentile

Solution:

Z score indicates that  how far from the mean  value is

Z score = ( Value - Mean)/Standard deviation

Verbal Reasoning section

Sophia Score = 160

Mean = 151

SD = 7

Z score for Verbal reasoning  = ( 160 - 151)/7

= 9/7

= 1.286

= 90 %  ( 90 percentile Score)

10%  students did better than her in Verbal reasoning section

Quantitative Reasoning section

Sophia Score = 157

Mean = 153

SD = 7.67

Z score for Verbal reasoning  = ( 157 - 153)/7.67

= 4/7.67

= 0.522

= 70 %  ( 70 percentile Score)

30% students did better than her in Quantitative reasoning section

Shopia performed better in verbal section compared to Quantitative section

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