The College Board reported that, in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 494.
A)97.5%
B)95%
C)2.5%
D)5%

Question

The College Board reported that, in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 494.
A)97.5%
B)95%
C)​2.5%
D)​5%

Quizplus · Accepted Answer

Using the empirical rule, we know that approximately 68% of scores fall within one standard deviation of the mean, 95% of scores fall within two standard deviations of the mean, and 99.7% of scores fall within three standard deviations of the mean. 
To find the percentage of students who scored less than 494, we need to convert this value to a z-score: z = (494 - 686)/96 = -1.99 
Using a standard normal distribution table, we can see that the percentage of students who scored less than a z-score of -1.99 is approximately 2.5%. Therefore, the answer is C) 2.5%.

The College Board Reported That, in 2014, the Mean Math