# Z Score Table

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Z Score Table
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 z-score
The number of standard deviations from the mean is called the z-score and can be
found by the formula

Z = x - m / s
Example

Find the z-score 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 z-score and Area
Often we want to find the probability that a z-score 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 z-score. This is exactly what we want.
Below are a few lines of the table.