The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored greater than 700.
A)97.5%
B)95%
C)2.5%
D)5%

Question

Quizplus · Accepted Answer

According to the empirical rule (or 68-95-99.7 rule) for a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Since a score of 700 is two standard deviations above the mean (500 + 2*100), this means that 95% of scores fall below 700. Therefore, only 5% of scores are above or below two standard deviations from the mean, but since we are only interested in those scoring higher than 700, we halve this percentage, resulting in 2.5% of students scoring greater than 700.

The College Board Originally Scaled SAT Scores So That the Scores