Learn how to calculate the area under the standard normal curve. This is an important skill, so study the following examples carefully.

To solve problems, you need the standard normal distribution table. So go ahead, print out the table and come back here.

example 1

Find the area under the curve between z = 0 and z = 1.32

If we look at the table we can see that 1.32 is nowhere to be found. However, we can divide 1.32 into 1.3 and 0.02.

Find 1.3 in the column for z on the left side of the table and find .02 in the row for z at the top of the table. Part of the table is reproduced below to show how to find the area.

Standard normal distribution table

The area under the standard normal curve between 0 and 1.32 is 0.4066

Standard normal distribution curve

This range can be interpreted as the probability that z assumes a value between 0 and 1.32.

In other words, area between 0 and 1.32 = P (0

Example # 2

Find P (-1.32

You just need to find the area under the normal curve between z = -1.32 and z = 0.

Since the normal curve is symmetrical about the mean value, the area from z = -1.32 to z = 0 is equal to the area from z = 0 to z = 1.32.

This area has already been calculated from example # 1, i.e. P (-1.32

Example # 3

Find the area under the standard normal curve to the right of z = 1.32

The area to the right of z = 1.32 is the blue shaded area as shown below.

Standard normal distribution curve

We also saw in the standard normal distribution lesson that the area in red plus the area in blue equals 0.5.

We have already calculated the area in red in Example 1 and it is equal to 0.4066. Let x be the area in blue.

0.4066 + x = 0.5

x = 0.5-0.4066 = 0.0934

Example # 4

Find the area between z = 1.32 and z = 2.54

This area is shown in green. Notice that area from z = 0 to z = 1.32 plus area in green = area from z = 0 to z = 2.54

To find the area from z = 0 to z = 2.54, use the table to see that it equals 0.4945.

Standard normal distribution curve

Area from z = 0 to z = 1.32 plus area in green = area from z = 0 to z = 2.54

The area from z = 0 to z = 1.32 is equal to 0.4066. Let x be the green area.

We get 0.4066 + x = 0.4945

x = 0.4945-0.4066 = 0.0879

Therefore the area is from z = 1.32 to z = 2.54 = 0.0879



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