Reading the Normal Distribution Tables

There are two different normal distribution tables. In our textbook they're labeled e.2 and e.11. (A third table on the page after the inside front cover of the book is identical to table e.2.)

What's the difference?

The first table (e.2) is the cumulative standard normal distribution table. With it, you can look up the area under the standard normal distribution function from -∞ to any particular z-score, either positive or negative.

Download a MS Word version of this table.

The second table (e.11) is the plain, old (not cumulative) standard normal distribution table. The values that you look up in that table are the area under the curve from the mean (0 since it's standardized) to your z-score.

You can really use either table in almost any scenario. I typically find the cumulative table easier to work with.

If A_c is the value in the cumulative table (e.2) and A_n is the value in the plain, old table (e.11), the relationship between the two tables is:

for z<0: A_c = 0.5 - A_n (using -z when looking up the value in e.11)

for z>0: A_c = A_n + 0.5

Reading Values from the Table
To use either standard normal distribution table, you first must calculate the z-score(s) that are of interest. The z-score is the number of standard deviations from the mean for your target value, X.

For example, if you have a normal distribution with mean 20 and standard deviation 3 and you want to know the probability of an observation being less than 22, you calculate the z-score as:

z = (X-μ)/σ = (22-20)/3 = 0.67

Our z-score tells us that we want to know the probability of an observation being less than 0.667 standard deviations from the mean. We turn to the cumulative standard normal distribution table to find this probability.

We go down the first column until we get one decimal point of accuracy (0.6) and then we move across the table to the row which gives us the second decimal point of accuracy (0.07). The value at the intersection is our answer!

So P(X<22) = 0.7486 = 74.86%