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.

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