### The Standard Normal (Z) Distribution

A very special family member normal distribution is called the standard normal distribution, or Z-distribution. The Z-distribution is used to help probabilities, and other types of problems when working in a normal distribution.
The standard normal (Z) distribution has a mean of zero and a standard deviation of 1; The graph shown in Figure 5-2. A value of Z-distribution data indicates the number of standard deviations above or below the average; These are called z-scores, or Z-value. For example, z = 1 in the Z-distribution represents an amount which is the first tie-standard Deviation above average. Similarly, z = -1 represents a value which is one standard deviation below the mean (indicated by the minus sign of the z-value).
Because the chance for a normal distribution almost impossible to calculate by hand, we use tables to find them. All the major results you need to find opportunities for a normal distribution can be summarized in a table based on the standard normal (Z) distribution. This table is the Z-table and in the Annex, Table A-1. All you need is a formula in your normal distribution (X) to convert the standard normal (Z) distribution, and you can use the Z-table for the time you need.
The general formula for changing a value of X, the value of Z. Take your x-value, the average pulling off, and dividing by the standard deviation; it gives you the corresponding z value.

For example, if X is a normal distribution with a mean 16 standard deviation 4, the value 20 will form the X-allotment of up to 20 to 16 divided by 4, where 1 is equal to the amount so 20 X-distribution corresponds to the value of 1 in the Z-distribution. Now use the Z-table opportunities for Z, which is equivalent to the corresponding probabilities for X. Table A-1 (Annex) is to be found the probabilities that Z is smaller than a value between -3 and +3.

To use the Z-table to find the time, do the following:

1. Go to the row with the leading digits of your z value and the first digit after the decimal point represents.

2. Go to the column representing the second decimal place value of z.

3. cutting the row and column as representing P (Z <z).

For example, suppose you want to look at P (Z <2.13). Use Table A-1 (attached) on the line for the column 2.1 and 0.03. Doc 2.1 and 0:03 to get together as a three-digit number 2.13. Crossing row and column to find the number: 0.9834. You will find that P (Z <2.13) = 0.9834.