By Saul McLeod, published May 30, 2019

A z-table, also called the standard normal table, is a mathematical table that allows us to know the percentage of values below (to the left) a z-score in a standard normal distribution (SND).

*Figure 1.* A standard normal distribution (SND).

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.

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.

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 (e.g. whole number and the first digit after the decimal point).

In this case it is 1.0. Then, we look up a remaining number across the table (on the top) which is 0.09 in our example.

*Figure 2.* Using a z-score table to calculate the proportion (%) of the SND to the left of the z-score.

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.

*Figure 3.* The proportion (%) of the SND to the left of the 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 which is 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.

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

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

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 together and subtract them from 1 (the total area of the SND.

Further Information

Z-Score Table (for positive a negative scores)
What is a Z-score
Finding the proportion of a normal distribution that is above a value by calculating a z-score and using a z-table (Kahn Academy Video)
Statistics for Psychology
What is a Normal Distribution in Statistics?
What a *p*-value Tells You About Statistical Significance
Statistics for Psychology Book Download

McLeod, S. A. (2019, May 30). *How to Use a Z-Table (Standard Normal Table)*. Retrieved from https://www.simplypsychology.org/z-table.html

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