Question

scores on the gre (graduate record examination) are normally distributed with a mean of 583 and a people taking the test who score between 481 and 685. the percentage of people taking the test who score between 481 and 685 is %

Explanation:

Step1: Calculate the difference between the mean and the scores

The mean is \( \mu = 583 \).
For \( x_1 = 481 \), the difference is \( 583 - 102 = 481 \).
For \( x_2 = 685 \), the difference is \( 583 + 102 = 481 \).

Step2: Apply the empirical rule

The empirical rule states that for a normal distribution, approximately \( 68\% \) of the data lies within \( \mu\pm\sigma \), \( 95\% \) within \( \mu\pm2\sigma \), and \( 99.7\% \) within \( \mu\pm3\sigma \).
Since \( 481 = 583 - 102 \) and \( 685 = 583 + 102 \), and \( 102 = 2\times51 \), this is within \( \mu\pm2\sigma \).

Answer:

\( 95\% \)