How to Use the Z-Score Table (Standard Normal Table) (2024)

Reading a Z-score table might initially seem tricky, but it becomes pretty straightforward once you understand the layout.

There are two kinds of Z-tables: for “less than” probabilities and for “more than” probabilities. The “less than” table is the most commonly used one.

A Z-score table shows the percentage of values (usually a decimal figure) to the left of a given Z-score on a standard normal distribution.

Here’s how you can read it:

1. Look at the Z-table. The left column will contain the first part of the Z-score (e.g., the whole number and the first digit after the decimal point). Go down this column until you find your Z-score’s first part.

2. Next, look at the top row of the Z-table. This row will contain the second part of the Z-score (the remaining decimal number). Go across this row until you find your Z-score’s second part.

3. The intersection of the row from the first part and the column from the second part will give you the value associated with your Z-score. This value represents the proportion of the data set that lies below the value corresponding to your Z-score in a standard normal distribution.

For example, imagine our Z-score value is 1.09.

First, look at the left side column of the z-table to find the value corresponding to one decimal place of the z-score. In this case, it is 1.0.

Then, we look up the remaining number across the table (on the top), which is 0.09 in our example.

The corresponding area is 0.8621, which translates into 86.21% of the standard normal distribution being below (or to the left) of the z-score.

To find the p-value, subtract this from 1 (which gives you 0.1379), then multiply by 2 (which gives you p = 0.2758).

The results are not statistically significant because the p-value is greater than the predetermined significance level (p = 0.05), and the null hypothesis is accepted.

Right of a positive z-score

To find the area to the right of a positive z-score, begin by reading off the area in the standard normal distribution table.

Since the total area under the bell curve is 1 (as a decimal value equivalent to 100%), we subtract the area from the table from 1.

For example, the area to the left of z = 1.09 is given in the table as .8621. Thus the area to the right of z = 1.09 is 1 – .8621. = .1379.

Left of a negative z-score

If you have a negative z-score, use the same table but disregard the negative sign, then subtract the area from the table from 1.

Right of a negative z-score

If you have a negative z-score, use the same table but disregard the negative sign to find the area above your z-score.

Finding the area between two z-scores

To find the area between two negative z-scores, we must first find the area (proportion of the SND) to the left of the lowest z-score value and the area (proportion of the SND) to the right of the highest z-score value.

Next, we must add these proportional values and subtract them from 1 (the SND’s total area of the SND.