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 \( \square \% \).

The GRE scores are normally distributed with a mean (μ) of 596 and a standard deviation (σ) of 93. To find the percentage of people who score between 410 and 782 using the 68-95-99.7 Rule, we first convert these scores to z-scores: For 410:   z = (410 − 596) / 93 = −186 / 93 = −2 For 782:   z = (782 − 596) / 93 = 186 / 93 = 2 According to the 68-95-99.7 rule, approximately 95% of data falls within ±2 standard deviations of the mean. Since 410 and 782 correspond to −2σ and +2σ, approximately 95% of the test takers score between these values. Thus, the percentage of people taking the test who score between 410 and 782 is 95%.