A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The percentile rank of a score of 667 is _________.
A) 3.14%
B) 96.78%
C) 3.22%
D) 96.86%

Question

Quizplus · Accepted Answer

First, we need to standardize the score using the formula:

z = (x - mean) / standard deviation

z = (667 - 500) / 90
z = 1.855

Next, we need to find the area under the standardized normal distribution curve to the left of z-score. This can be done using a table or a calculator. Using a calculator, we can find the area to be:

P(z < 1.855) = 0.9678 or 96.78%

Finally, we need the percentile rank, which is the percentage of scores that fall below the given score. Since we want the percentage above the score, we subtract the area from 100%:

Percentile rank = 100% - 96.78% = 3.22%

Therefore, the answer is D (96.86%).

A Testing Bureau Reports That the Mean for the Population