# B \(z\)-score tables

This Appendix contains \(z\)-score tables.

These tables provide the area *to the left* of a given \(z\)-score associated with a normal distribution
(Appendix B.1),
or the \(z\)-score such that a given area is to the left (Appendix B.2).

The online version of this book has online tables, which are easier to use.

## B.1 When the \(z\)-score is known, and the area is sought

The table gives the probability (area) that a \(z\)-score is *less* than a given value.
For example:
for \(z = -1.38\), the area *less than* \(z = -1.87\) is about \(0.0838\), or about \(8.38\)%.

To use this table, enter the \(z\)-score in the search box *under* the `z.score`

column.
The area will be shown.
The table includes \(z\)-values between \(-4\) and \(4\).
(Alternatively, you can search through the table manually.)

These Tables work with two decimal places.
As an example, then, consider finding the area to the *left* of \(z=-2.00\).
In the tables, the value `-2`

is entered in the search region, just under the column labelled `z.score`

(see the animation below).
After pressing `Enter`

, the answer is shown in the column headed `Area.to.left`

: the probability of finding a \(z\)-score less than \(-2\) is \(0.0228\), or about \(2.28\)%.

The hard-copy tables work differently.
On the tables, look for \(-2.0\) in the *left* margin of the table, and for the second decimal place (in this case, \(0\)) in the *top* margin of the table (see the animation below).
Where these intersect is the area (or probability) *less than* this \(z\)-score.
So the probability of finding a \(z\)-score less than \(-2\) is \(0.0228\), or about \(2.28\)%.

## B.2 When the area is known, and the \(z\)-score is sought

The table gives the \(z\)-score such that a given probability (area) is to the left of the \(z\)-score. For example: Look up an area of \(0.10\) (i.e., \(10\)%), and the corresponding \(z\)-score is \(z = -1.282\). That is, the area to the left of \(z = 1.282\) is about \(10\)%.

To use this table, enter that area *to the left* in the search box *under* the `Area.to.left`

column.
The corresponding \(z\)-score will be shown.
(Alternatively, you can search through the table manually.)

When the \(z\) score was known, the tables in Appendix B.1 were used.
However, when working backwards, the tables in Appendix B.2 are used: enter the area to the left in search box under `Area.to.left`

, and the corresponding \(z\)-scores appears under the `z.score`

column (see the animation below).

The hard copy tables work differently.
When the \(z\) scores (which appear in the *margins* of the tables; see Sect. 21.8) is known, the *area* appears in the *body* of the table.
However if the area (or probability), which is in the *body* of the table, is known, the corresponding \(z\)-score is found in the *margins* of the table, and hence the observation \(x\); see the animation below.