Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 596 and a standard deviation of 93 . Use the 68-95-99.7 Rule to find the percentage of people taking the test who score between 410 and 782 . The percentage of people taking the test who score between 410 and 782 is \( \square \% \).

To find the percentage of people scoring between 410 and 782 on the GRE using the 68-95-99.7 Rule, we first calculate how many standard deviations these scores are from the mean. The mean is 596 and the standard deviation is 93. 1. For 410: \[ z = \frac{410 - 596}{93} = \frac{-186}{93} \approx -2 \] 2. For 782: \[ z = \frac{782 - 596}{93} = \frac{186}{93} \approx 2 \] According to the 68-95-99.7 Rule, about 95% of the data falls within two standard deviations from the mean. Therefore, the percentage of people taking the test who score between 410 and 782 is approximately \( 95\% \).