If Z is a standard normal random variable,the area between Z = 0.0 and Z =1.20 is 0.3849,while the area between Z = 0.0 and Z = 1.40 is 0.4192.What is the area between Z = -1.20 and Z = 1.40?
A)0.8041
B)0.0808
C)0.1151
D)0.0343

Question

Quizplus · Accepted Answer

The area between Z = -1.20 and Z = 1.40 is found by adding the area from Z = 0 to Z = 1.20 (0.3849) and the area from Z = 0 to Z = 1.40 (0.4192), then subtracting the overlap (the area from Z = 0 to Z = 1.20, since it's included in both calculations). However, since the normal distribution is symmetric, the area from Z = 0 to Z = -1.20 is the same as from Z = 0 to Z = 1.20. Therefore, we simply add the area from Z = 0 to Z = 1.20 (0.3849) to the area from Z = 0 to Z = 1.40 (0.4192) to get the total area, which equals 0.8041.

If Z Is a Standard Normal Random Variable,the Area Between