Question

As the SAT is used for college admissions, the GRE is used for graduate school admissions. A sample of verbal and quantitative scores from the GRE are both normally distributed, with the values of u and o are given below. Kevin scored 610 on the verbal section and 700 on the quantitative section. Use the standard deviation as a unit of measurement to compare Kevin's verbal and quantitative scores on the GRE.

Answer 1

Kevin's verbal score (610), although, lower than the Quantitative score (700), is comparatively/relatively a better score when compared to the gemeral performance of all people that sat for the same exams.

Explanation:

Missing from the question

The mean score for Verbal Reasoning section was 462 with a standard deviation of 119, and the mean score for the Quantitative Reasoning was 584 with a standard deviation of 151.

To truly compare these two scores, we first need to standardize them.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For the verbal section

Mean = 462

standard deviation = 119

z = (x - μ)/σ = (610 - 462)/119 = 1.24

For the Quantitative section

Mean = 584

standard deviation = 151

z = (x - μ)/σ = (700 - 584)/151 = 0.77

Using the normal distribution tables

P(z < 1.24) = 0.893 = 89.3 percentile

P(z < 0.77) = 0.779 = 77.9 percentile

From the results obtained, Kevin's verbal scores of 610, although lower than the Quantitative score of 700, is 1.24 standard deviations greater than the mean, thereby putting this score in the 89.3 percentile amongst all those that sat for the same verbal section.

The quantitative score of 700 is 0.77 standard deviations greater than the mean, belonging to a percentile of 77.9 of all those that wrote that quantitative section.

Hope this Helps!!!