Three Normal Distributions

    A normal distribution is described by its mean (, read as "x bar") and standard deviation (s), as ± s. The interval between ±1 s always includes 68.27% of the area under the curve, ±2 s includes 95.45%, and ±3 s includes 99.73%. Alternatively, 50% of the area lies between ±0.674 s, 95% between ±1.960 s, and 99% between ±2.576 s. This is true whether the distribution is tall (A) or wide (B) or offset to a higher mean (C). [The parametric mean and standard deviation are written µ ± ].

Figure ©2002 by Griffiths et al.; all text material ©2012 by Steven M. Carr