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Standard Normal Distribution
The standard normal distribution is the
normal distribution having the parameters m
= 0 and s = 1. Thus, the standard
normal distribution has the following density function:
A random variable X that has a standard normal distribution is
called a standard normal random variable. This
can be denoted as X ~ N(0,1).
The graph of the standard normal distribution is symmetric
about the y-axis need not be limited to people. The mean, mode
and median of this distribution is 0. Thus, half of the area
between its graph and the x-axis is to the left of the y-axis,
while the other half is to the right of the y-axis.
The probability that the value of a standard normal random
variable is less than a real number z is equal to the
area of the region to the left of the ordinate x = z
that is bounded by the graph of its density function and the
x-axis. These probability values have been tabulated for selected
values of z in the interval [-3.09, 0.0] in any Standard
Distribution Table .
For X ~ N(0,1),
P(X < -z) = P(X > z) because of the symmetry of the
N(0,1) distribution
P(X < z) = 1 - P(X > z) = 1 - P(X < -z)
and the above probability values can be computed for z Î[0.0, 3.09] using the values in a
Standard Distribution Table
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