Statistical Process Control and Data Analytics, 8th Edition

Appendix AThe normal distribution and non-normality

The mathematical equation for the normal curve (alternatively known as the Gaussian distribution) is:

$y=\frac{1}{\sigma \sqrt{2\pi }}{\text{e}}^{-{\left(x-\overline{x}\right)}^2/2{\sigma }^2},$

where y = height of curve at any point x along the scale of the variable

• σ = standard deviationThe dispersion between two or more data. of the populationThe full set of data from which samples may be taken.
• $\overline{x}$ = average value of the variable for the distribution
• π = ratio of circumference of a circle to its diameter $(\pi =3.1416)$
• If $z=(x-\overline{x})/\sigma ,$ then the equation becomes:

$y=\frac{1}{\sigma \sqrt{2\pi }}{\text{e}}^{-z^2/2}.$

The constant $1/\sqrt{2\pi }$ has been chosen to ensure that the area under this curve is equal to unity, or probabilityA measure of the likelihood of an occurrence or incident. 1.0. This allows the area ...