The Standard Normal Distribution
The standard normal distribution is a normal distribution
with mean mu = 0 and Std. Deviation sigma = 1. Fifty percent of the total area under the curve is to the left of 0 and 50 % of the total area under the curve is to the right of 0.
The total area under the curve is 1.0 The numbers along the horizontal axis are z-Scores.
Finding Areas Under The Standard Normal Curve
Recall from earlier work that finding probabilities of continuous
random variables involves measuring areas under density functions. Since our
present work involves normal curves or normal density functions, we must learn
how to find areas under normal curves. These areas or probabilities are usually
provided in the form of tables
There are two tables in your text which deal with z scores and areas under the
standard normal curve. One table is found on the inside front cover of your text
and gives the area under the standard normal curve from negative infinity to a
given z value. The second table is found in the appendix page A8 and gives the
area under the standard normal curve from z = 0 to a given positive z. Due to
the symmetry of the standard normal curve, this table can be use for finding
areas under the standard normal curve from z = 0 to a negative z value.
Examples:
1.Find the area between z = 0 and z = 1.6
From table A8: Read directly from table 0.4452
From table on inside front cover: 0.9452 - 0.5000 =
0.4452
2. Find area between z = 0 and z = 1.64
From table A8: Read directly from table 0.4495
From table on inside front cover: 0.9495 - 0.5000 = 0.4495
3. Find the area to right of 1.64
From table A8: 0.5000 - 0.4495 = 0.0505
From table on inside front cover: 1.0000 - 0.9495 = 0.0505
4.Find the area to left of z = -.50
From table A8: 0.5000-0.1915 = 0.3085
From table on inside front cover: read directly from table 0.3085
5. Find the area between z = 0.46 and z = 2.11
From table A8: 0.4826 - 0.1772 = 0.3054
From table on inside front cover: 0.9826 - 0.6772 = 0.3054
Knowing how to find areas under the standard normal distribution will enable
one to find areas under any normal distribution.