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:
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.
