Question

The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 110, while the mean score was 76 and the standard deviation was 7. 55 62 69 76 83 90 97 Distribution of Test Scores What is the approximate percentage of students who scored lower than 55 on the test? % What is the approximate percentage of students who scored between 62 and 90 on the test? % What is the approximate percentage students who scored between 69 and 83 on the test? % What is the approximate percentage of students who scored higher than 90 on the test?

Answer 1

from empirical rule:

1)

approximate percentage of students who scored lower than 55 on the test :

probability =P(X<55)=(Z<(55-76)/7)=P(Z<-3)=0.15 %

2)

approximate percentage of students who scored between 62 and 90 on the test :

probability =P(62<X<90)=P((62-76)/7)<Z<(90-76)/7)=P(-2<Z<2)=95 %

3)

approximate percentage students who scored between 69 and 83 on the test :

probability =P(69<X<83)=P((69-76)/7)<Z<(83-76)/7)=P(-1<Z<1)=68 %

4)

approximate percentage of students who scored higher than 90 on the test :

probability =P(X>90)=P(Z>(90-76)/7)=P(Z>2)=1-P(Z<2)=2.5 %