Z Tables

A Z table uses statistical information taken from a sampling of data to make predictions about the overall population from which the sample was taken.  Specifically, the Z table estimates how much data (expressed as a probability or percentage) will fall above or below a given value of interest in the population.  Z table predictions assume that the population data is normally distributed, and that the sample data is in fact representative of the population.

standard normal curve and area provided by the z tables on this site

Z tables are used in a number of applications where predictions must be made based on limited data.  For example, manufacturing businesses use Z tables for predicting long term defect rates on products, based on data sampled during or after the production process.

How to Read a Z Table

1. Every Z table should have a diagram that shows exactly which area is being displayed on the table.  For example, the Z tables referenced on this site show the following diagram on each table -

a diagram similar to this should accompany a Z table

2.  Check to ensure that your sample data is normally distributed.   If the data is not normally distributed, then there is a good chance that any predictions made with the Z table will be erroneous.  Also plot the data in a histogram to look for any abnormalities (data entry errors, etc) that will need to be addressed.

3.  Calculate the average and standard deviation of the sample data.

4.  Calculate the Z value using the formula Z= (x-μ)/σ, where x is the point of interest, μ us the average, and σ is the standard deviation.

5.  Look up the value on the Z table to find the appropriate area.  For example, a Z value of -1.94 (highlighted in yellow) has an area of 0.026, or 2.6% of all data, to the left of Z.  Note the that -1.9 Z value is found by moving down Z column, and then the -1.94 value is found by staying in the 1.9 row and moving over to the 0.04 column.

how to find a z value on a z table