Question

Scores on the verbal portion of the GRE follow a normal distribution with a mean of 500 and standard deviation of 115.

Suppose your score on the exam is 650.

First, record the z-score associated with your score of 650. The z-score for 650 is __________

Second, determine the proportion (or percentage) of test-takers that you did better than ______________

Answer 1

Let X denote the Scores on the verbal portion of the GRE.

Given that

The Z score can be obtained by standardizing the normal variable into standard normal using the formula:

Substituting the values, for X = 650

= 1.30

Hence, the Z score associated with the score of 650 = 1.30

To find proportion (or percentage) of test-takers that the student did better than can be determined by computing the area to the left of the Z score from standard normal table:

Hence, from the table above, the required area / percentage is the figure corresponding to row 1.3 and column 0.00.

i.e. Proportion (or percentage) of test-takers that the student did better than = 90.32%