A random variable X has a normal distribution with mean m and standard error s if for every pair of numbers a ≤ b, the chance that a < (X−m)/s < b is

P(a < (X−m)/s < b) = area under the normal curve between a and b.

If there are numbers m and s such that X has a normal distribution with mean m and standard error s, then X is said to have a normal distribution or to be normally distributed. If X has a normal distribution with mean m=0 and standard error s=1, then X is said to have a standard normal distribution. The notation X~N(m,s²) means that X has a normal distribution with mean m and standard error s; for example, X~N(0,1), means X has a standard normal distribution.