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.
Comments
Post a Comment
any suggestion on my side