Use the standard normal distribution to find p(-2.25 < z < 1.25).

Solution:

The probability of the value z (standard normal variable) lying between -2.25 and 1.25 is diagrammatically represented by the figure below:

The shaded area (ABECD) represents the area that gives the value of the expression p(-2.25 < z < 1.25).

The area ABECD comprises two shaded components ABEF and EFDC.

The area ABEF is found out from the tables of normal distribution. The area under the curve is 0.4878 (from the tables).

The area EFDC is also found out from the normal distribution tables and is given as 0.3944.

The probability p(-2.25 < z < 1.25) = 0.4878 + 0.3944 = 0.8822

The probability of the value lying between z = -2.25 and 1.25 is 88.22% or 0.8825

Use the standard normal distribution to find p(-2.25 < z < 1.25).

Summary:

From the standard normal distribution the value of p(-2.25 < z < 1.25) = 88.22% or 0.8825