Z Score Table
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Z Score Table
Definition of the Standard Normal Distribution
The Standard Normal distribution fol ows a normal distribution and has mean 0 and
standard deviation 1
Notice that the distribution is perfectly symmetric about 0.
If a distribution is normal but not standard, we can convert a value to the Standard
normal distribution table by first by finding how many standard deviations away the
number is from the mean.
The zscore
The number of standard deviations from the mean is called the zscore and can be
found by the formula
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Z = x  m / s
Example
Find the zscore corresponding to a raw score of 132 from a normal distribution with
mean 100 and standard deviation 15.
Solution
We compute
Z = 132  100 / 15
Z = 2.133
The zscore and Area
Often we want to find the probability that a zscore wil be less than a given value,
greater than a given value, or in between two values. To accomplish this, we use the
table from the textbook and a few properties about the normal distribution.
Example: Find = P(z < 2.37)
Solution: We use the table. Notice the picture on the table has shaded region
corresponding to the area to the left (below) a zscore. This is exactly what we want.
Below are a few lines of the table.
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