How to Find the Indicated Area Under the Standard Normal Curve


One of the most common questions in elementary statistics is:

“Find the indicated area under the standard normal curve.”

These types of questions can be answered by using values found in the z table. This tutorial explains how to use the z table to answer the following four types of these questions:

  • Find the area under the curve less than some value.
  • Find the area under the curve greater than some value.
  • Find the area under the curve between two values.
  • Find the area under the curve outside of two values.

Example 1: Find the Indicated Area Less Than Some Value

Question: Find the area under the standard normal curve to the left of z = 1.26.

Solution: To answer this question, we simply need to look up the value in the z table that corresponds to 1.26:

Find the indicated area under the standard normal curve

The area under the standard normal curve to the left of z = 1.26 is 0.8962.

Example 2: Find the Indicated Area Greater Than Some Value

Question: Find the area under the standard normal curve to the right of z = -1.81.

Solution: To answer this question, we simply need to look up the value in the z table that corresponds to -1.81 and subtract it from 1:

The area under the standard normal curve to the right of z = -1.81 is 1 – .0351 –  0.9649.

Example 3: Find the Indicated Area Between Two Values

Question: Find the area under the standard normal curve between z = -1.81 and z = 1.26

Solution: To answer this question, we simply need to subtract the area to the left of z = -1.81 from the area to the left of 1.26.

In the previous examples, we found that the area to the left of z = -1.81 was .0351 and the area to the left of z = 1.26 was .8962. 

Thus, the area under the standard normal curve between z = -1.81 and z = 1.26 is .8962 – .0351 = 0.8611.

Example 4: Find the Indicated Area Outside of Two Values

Question: Find the area under the standard normal curve outside of z = -1.81 and z = 1.26

Solution: To answer this question, we need to add up the area to the left of z = -1.81 and the area to the right of z = 1.26.

The area to the left of z = -1.81 is .0351 and the area to the right of z = 1.26 is 1-.8962 = .1038.

Thus, the area between z = -1.81 and z = 1.26 is .0351 + .1038 = .1389.

Bonus: The Standard Normal Curve Area Calculator

You can use this calculator to automatically find the area under the standard normal curve between two values.

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