Z Value
by
Forest Edward Thompson III (UoPhx 2008)
A normal
distribution can be transformed into a standard normal distribution by
discovering the zvalue. The zvalue is determined by
subtracting the (X) value from the mean, and divided by the standard
deviation.
The zvalue is also
known as:
§
z scores
§
standard normal values
§
normal deviate
§
standard normal deviate
§
z statistics
The Standard Normal Value
formula is:
·
X is the value of any observation, measurements, or
numbers
·
Mu is the mean of the distribution
·
S is the standard deviation of the distribution
The
Standard Normal Value formula is used to find the zvalue. The zvalue
is then used to determine the probability for the standard normal
probability distribution. This is discovered by using the statistical
graph for the “Areas under the Normal Curve” or the “Standard Normal
Probabilities”.
This is an example of the
“Areas under the Normal Curve” or the “Standard Normal Probabilities”
chart:
Lind, D. A. & Marchal, W. G. & Wathen, S. A. (2004). Statistical
techniques in business and economics, 12e: Appendix D, pg. 720: Areas
Under the Normal Curve. New York: The McGrawHill Companies
To understand how to use the
chart:
1.
Use the Standard Normal Value formula to discover the zvalue
2.
Once the zvalue is discovered refer to your chart to understand its
probability
3.
Locate the zvalue number on the left side of the chart going
vertically (using this chart as an example the zvalue numbers are
from point 0.0 to 3.0 in the vertical column)
4.
Once the zvalue number has been discovered in the vertical column,
then use the horizontal row to discover the second part of the
zvalue (using this chart as an example the zvalue numbers are from
point 0.00 to 0.09 in the horizontal row)
Example: the zvalue
is 2.62
Using the chart, find 2.6
in the vertical column and 0.02 in the horizontal row. If z = 2.62, then
P (0 to z) = 0.4956
These are internet links that will help with more detailed information
on normal probability distribution, bellshape curve, zvalue, charts,
and statistical calculators:
http://www.cas.buffalo.edu/classes/psy/segal/2072001/zdist&corr/zdist.htm
http://www.math.com/tables/stat/distributions/zdist.htm
http://stattrek.com/Lesson2/Normal.aspx
http://davidmlane.com/hyperstat/z_table.html
http://www.math.csusb.edu/faculty/stanton/m262/normal_distribution/normal_distribution.html
http://faculty.uncfsu.edu/dwallace/szscore.html
Reference
Lind, D. A.
& Marchal, W. G. & Wathen, S. A. (2004). Statistical techniques in
business and economics, 12e: Chapter 7: Continuous Probability
Distributions. New York: The McGrawHill Companies
