http://www.ck12.org Chapter 5. Normal Distribution
Z-Tables
Before software and graphing calculator technology was readily available, it was common to use tables to approx-
imate the amount of area under a normal density curve between any two givenz−scores. We have included two
commonly used tables at the end of this lesson. Here are a few things you should know about reading these tables:
The values in these tables are all in terms ofz−scores, orstandardized, meaning that they correspond to a standard
normal curve in which the mean is 0 and the standard deviation is 1. It is important to understand that the table
shows the areasbelowthe givenz−score in the table. It is possible and often necessary to calculate the areaabove,
orbetweenz−scores as well. You could generate new tables to show these values, but it is just as easy to calculate
them from the one table.
The values in these tables can represent areas under the density curve. For example,.500 means half of the area
(because the area of the total density curve is 1). However, they are most frequently expressed as probabilities, e.g.
.500 means the probability of a randomly chosen value from this distribution being in that region is.5, or a 50%
chance.
Z−scores must be rounded to the nearest hundredth to use the table.
Mostz−score tables do not go much beyond 3 standard deviations away from the mean in either direction because
as you know, the probability of experiencing results that extreme in a normal distribution is very low.
Table 5.5 shows those below the mean and Table 5.6 shows values ofz−scores that are to the right of the mean. To
help you understand how to read the table, look at the top left entry of Table 5.6. It reads.500.
Think of the table as a stem and leaf plot with the stem of thez−scores running down the left side of the table and
the leaves across the top. The leaves represent 100ths of az−score. So, this value represents az−score of 0.00. This
should make sense because we are talking about the actual mean.
Let’s look at another common value. In Table 5.6 find thez−score of 1 and read the associated probability value.