Standard Normal Quantile

The p-th quantile (or 100p-th percentile) of the standard normal distribution is the solution to

i.e.,

Notes:

• The first equation above tells us that the area under the standard normal density curve to the left of the p-th quantile is equal to p. This is illustrated below for the case of the 0.95-th quantile.
  
  
• The second equation above expresses the quantile formally as the inverse function corresponding to the standard normal cdf. For practical purposes, you can restrict the domain of this inverse function to the open interval (0,1).
• Use a statistical table or suitable computer software to obtain values of the standard normal quantile. For example, using Table 6, we find that
  i.e., the 0.975-th quantile or 97.5-th percentile of the standard normal distribution is about 1.96.