# Thread: Percentage points of the normal distribution

1. ## Percentage points of the normal distribution

Can anyone explain and show how to use Percentage points of the normal distribution??

If you can give me some examples of using Percentage points of the normal distribution, i would really appreiciate it.

Thank you.

Here is percentage points of the normal distribution.

PERCENTAGE POINTS OF THE NORMAL DISTRIBUTION
The values z in the table are those which a random variable Z ∼ N(0, 1) exceeds with probability p;
that is, P(Z > z) = 1 − Φ(z) = p.
p　　 　z　　　 p　　　 z
0.5000 0.0000 0.0500 1.6449
0.4000 0.2533 0.0250 1.9600
0.3000 0.5244 0.0100 2.3263
0.2000 0.8416 0.0050 2.5758
0.1500 1.0364 0.0010 3.0902
0.1000 1.2816 0.0005 3.2905

2. Are you asking how to find percentile points of a non-standard normal random variable? The values you posted are of a st normal.

The transformation between a normal and a st normal is

$\displaystyle Z={X-\mu_X\over \sigma_X}$ where $\displaystyle \mu_X$ is the expectation of X and $\displaystyle \sigma_X$ the standard deviation of X.