Normal distribution

The normal distribution was described in 1820 by Carl Friedrich Gauss. It occurs when a large number of independent random variables which possess the same expected value and the same variance are summed.

The following table reproduces selected quantiles (also called alpha-quantiles) for the normal distribution:

alpha 0.1 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005
X 1.2816 1.6449 1.9600 2.3263 2.5758 2.8070 3.0902 3.2905

Reference: Christian Schiestl, Pseudozufallszahlen in der Kryptographie, in Klagenfurt, 1999.