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 ÃŽ[0.0, 3.09] using the values in a Standard Distribution Table
