Question

The GRE is an entrance exam that most students are required to take upon entering graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.

What percent of scores were between 286 and 322? Round your answer to the nearest whole number.

Answer 1

Answer:82% of scores are between 286 and 322

Explanation:

Answer 2

The GRE Scores are represented as ~N(310,12)

In order to find the proportion of scores between 286 and 322, we need to standardize the scores so we can use the standard normal probabilities. Thus, we will find the z-score.

`z-score = (286 - 310)/(12) = -2`

`z-score = (322 - 310)/(12) = 1`

By looking on the standard normal probabilities table, we find the proportion of scores less than -2.
P(z < -2) = 0.0228
Then, we find the proportion of scores less than 1.
P(z < 1) = 0.8413

To find the proportion between -2 and 1, we subtract the two.
P(-2 < z < 1) = 0.8413 - 0.0228 = 0.8185 = 81.85%

Therefore, 82% of scores are between 286 and 322