Normal Quantile

Suppose

The p-th quantile of the above normal distribution is the solution to the equation

i.e.,
where z_p is the corresponding standard normal quantile.

Notes:

• The p-th quantile in the above definition is also referred to as the 100p-th percentile of the (general) normal distribution.
• By definition, the area under a normal density curve to the left of the p-th quantile is equal to p. You can visualize this in a manner similar to that given earlier for the 0.95-th quantile of the standard normal distribution.
• Values for x_p may be obtained once you have values for the corresponding standard normal quantiles, z_p, and these may be found using Table 6, for example, or an appropriate computer software.