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 70 and the standard deviation was 15.



What is the approximate percentage of students who scored lower than 25 on the test?
%

What is the approximate percentage of students who scored between 55 and 70?
%

What is the approximate percentage of students who scored higher than 100 on the test?
%

What is the approximate percentage of students who scored between 40 and 100 on the test?
%

Answer 1

Given,

= 70, = 15

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X < 25) = P( Z < 25 - 70 / 15 )

= P( Z < -3)

= 1 - P( Z < 3)

= 1 - 0.9987

= 0.0013

= 0.13%

b)

P( 55 < X < 70) = P( X < 70) - P( X < 55)

= P( Z < 70 - 70 / 15) - P( Z < 55 - 70 / 15)

= P( Z < 0) - P( Z < -1)

= P( Z < 0) - ( 1 - P( Z < 1) )

= 0.5 - ( 1 - 0.8413)

= 0.3413

= 34.13%

b)

P( X > 100) = P( Z > 100 - 70 / 15)

= P( Z > 2)

= 1 - P( Z < 2)

= 1 - 0.9772

= 0.0228

= 2.28%

d)

P( 40 < X < 100) = P( X < 100) - P( X < 40)

= P( Z < 100 - 70 / 15) - P( Z < 40 - 70 / 15)

= P( Z < 2) - P( Z < -2)

= P( Z < 2) - ( 1 - P( Z < 2) )

= 0.9772 - ( 1 - 0.9772)

= 0.9545

= 95.45%