4.3.2 Percentiles of the Standard Normal Distribution

For any $p$ between 0 and 1, Appendix Table A. 3 can be used to obtain the $\left(100p\right)$th percentile of the standard normal distribution.

EX 4.14 percentile of standard normal distribution

In general, the $\left(100p\right)$ th percentile is identified by the row and column of Appendix Table A.3 in which the entry $p$ is found (e.g., the 67 th percentile is obtained by finding .6700 in the body of the table, which gives $z=.44$ ). If $p$ does not appear, the number closest to it is typically used, although linear interpolation gives a more accurate answer. For example, to find the 95th percentile, look for .9500 inside the table. Although it does not appear, both .9495 and .9505 do, corresponding to $z=1.64$ and 1.65, respectively. Since .9500 is halfway between the two probabilities that do appear, we will use 1.645 as the 95th percentile and -1.645 as the 5th percentile.