The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 130, while the mean score was 70 and the standard deviation was 13.

Question

31 44 57 70 83 96 109

(distribution of test scores)

What is the approximate percentage students who scored between 57 and 83 on the test?

What is the approximate percentage of students who scored lower than 31 on the test?

What is the approximate percentage of students who scored between 57 and 70?

What is the approximate percentage of students who scored between 31 and 70 on the test?

Answer 1

between 57 and 83 are about 68% of the scores as 57 and 83 are within 1 standard deviation from the mean, and by the empirical rule

that's 68%

below 31 is 3 standard deviations below the mean, and by the empirical rule, 99.7% are within 3 standard deviations. but divide 1-.997 in half = .003/2 = .0015

= .15% are below 31

between 57 and 70 is half 68 = 34%

between 31 and 70 is half 99.7 = 49.85%