The normal distribution, or approximations of it, arise frequently in nature (this is partly explained by the central limit theorem).  Since it also has many convenient mathematical properties it is the most commonly used continuous distribution.

For this distribution, 68.2% of the probability is within 1 standard deviation of the mean, 95.4% is within 2 standard deviations, and 99.74% is within 3 standard deviations.

If μ = 0, σ = 1 it is known as a “standard normal” distribution.