Question

The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 140, while the mean score was 75 and the standard deviation was 15. 30 45 105 120 60 75 90 Distribution of Test Scores Using the Empirical Rule, What is the approximate percentage of students who scored between 45 and 105 on the test? % What is the approximate percentage of students who scored higher than 105 on the test? 19 What is the approximate percentage of students who scored between 60 and 75? % What is the approximate percentage of students who scored higher than 120 on the test? %

Answer 1

Answer

The Empirical Rule

For data with a bell shaped or normal distribution

About 68% of the data is within 1 standard deviation of the mean.

About 95% of the data is within 2 standard deviations of the mean.

About 99.7% of the data is within 3 standard deviations of the mean.

* 95%.53 X let X be the test score of students. Criven that XGN (102) with u = 75 and o = 15. Since 4-20 = 75-30=45, and 4+20=75+30=105, hence of students's core lies b/w 45 und 105 on the test 951 since of students scored b/w 454 105, and 57: beyond this approx of scores lies, so using symmetricity 2.511 of Normal distribution about student scored highes on the test * Since y-0=60 & 4+0 = 90,80 by empirical rule, approx 68-1 of student scored b/w 60 & 9o, so using symmetricity of the distribution, approx 2444 student scored 6/W 60475 Using empirical rule, we know approx 99.7'% Student scored 6164-30 = 30 and 4+30 = 120, 30 approx 0.05% Student scored higher than 120 on the test than los