You can use the z-table to find a set of “less-than” probabilities for a wide range of z -values. To use the z - table to find probabilities::

1. Go to the row that represents the first digit and the first digit after the decimal point of your z -value. (e.g 0.9 in 0.93)

2. Go to the column that represents the second digit after the decimal point of your z -value. (e.g 3 in 0.93, this will be 0.03 in the column)

3. Intersect the row and column from Steps 1 and 2.

For example, suppose you want to find the probability of z-score less than 1.44 denoted as p ( Z < 1.44). Using the second Z -table below, find the row for 1.4 and the column for 0.04. Intersect that row and column to find the probability: 0.92507. Therefore p ( Z < 1.44) = 0.92507.

The area under any normal curve (including the standardized normal curve) is 1, that means that, p ( Z < 1.44) + p ( Z > 1.44) =1. Therefore, the probability of z-score greater than 1.44 i.e. p ( Z > 1.44) = 1 – p ( Z < 1.44) which equals 1 – 0.92507 which equals 0.07493.

Suppose you want to look for p ( Z < –1.44). You find the row for –1.14 and the column for 0.04. Intersect the row and column and you find 0.07493. That means p ( Z < –1.44) = 0.07493. This happens to be the same as the value of p ( Z > +1.44). This is because the normal distribution is symmetric. So the tail of the curve below –1.44 representing p ( Z < –1.44) looks exactly like the tail above 1.44 representing p ( Z > +1.44).

You can also do a reverse lookup, assuming you are told that the age of grade 1 kindergarten pupils in Kampala city is normally distributed with a mean of 6 years. If only 0.71% (same as 0.0071) of the pupils are 8 years and above, what is the z-score?

We can look within the negative box for the z-score closest to 0.0071. In this case -2.45, but because we are looking at the right-tailed test, we get rid of the negative sign i.e.z-value = 2.45 (Note: if it was a left-tailed test e.g. 0.71% of them were less than 3 years old, we will use the value as-is) OR

We can look within the positive table, for the value that corresponds to 1-0.0071 = 0.99286 (we do this because the standard normal table always gives you values to the left, so to get values to the right, you will have to remove from 1). The value that corresponds to this will be 2.45.

To make things easier, you can also use a "z-score from p-value" or a "p-value from z-score" calculator online.