Editing Standard score (section)

=== Prediction intervals===
{{anchor|prediction intervals}}
The standard score can be used in the calculation of [[prediction interval]]s. A prediction interval [''L'',''U''], consisting of a lower endpoint designated ''L'' and an upper endpoint designated ''U'', is an interval such that a future observation ''X'' will lie in the interval with high probability <math>\gamma</math>, i.e.

:<math>P(L<X<U) =\gamma,</math>

For the standard score ''Z'' of ''X'' it gives:<ref>{{cite book |author=E. Kreyszig |author-link=Erwin Kreyszig |edition=Fourth |year=1979 |title=Advanced Engineering Mathematics |publisher=Wiley |isbn=0-471-02140-7 |page=880, eq. 6}}</ref>
:<math>P\left( \frac{L-\mu}{\sigma} < Z < \frac{U-\mu}{\sigma} \right) = \gamma.</math>
By determining the quantile z such that
:<math>P\left( -z < Z < z \right) = \gamma</math>
it follows:
:<math>L=\mu-z\sigma,\ U=\mu+z\sigma</math>