The normal distribution is a probability density which is bell-shaped, symmetrical, and single peaked. The mean, median and mode coincide and lie at the center of the distribution. The two tails extend indefinitely and never touch the x-axis (asymptotic to the x-axis). A normal distribution is fully specified by two parameters – mean and the standard deviation.
A Standard Normal Distribution is one that has zero mean, and standard deviation of 1. Data that are standardized (subtract the mean, divide by the standard deviation) are often compared to the Standard Normal distribution, to see where an individual observation lies relative to it. The formula for the Standard Normal probability density function (PDF) is
For a finite population of size N, where μ is population mean,
σ^2=1/N ∑_(i=1)^N▒(x_i-μ)^2 , or
If X is a random variable with mean μ,