The College Board reported that 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

Quizplus · Accepted Answer

According to the empirical rule, approximately 68% of the scores lie within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

To find the percentage of students who scored less than 494, we need to compute the z-score for this value:

z = (494 - 686) / 96 = -2

This tells us that a score of 494 is 2 standard deviations below the mean.

Since we're looking for the percentage of scores that are below 494, we can use the empirical rule to calculate this as:

P(score < 494) = P(z < -2)

This probability corresponds to the area under the normal distribution curve to the left of z = -2.

Using a normal probability table or calculator, we can find that P(z < -2) = 0.0228, which is approximately 2.28%.

Therefore, the percentage of students who scored less than 494 on the Math Level 2 SAT subject test is about 2.5%, which corresponds to choice C.

The College Board Reported That the Mean Math Level 2