Chi-squared Distribution

If X₁,X₂,…,X_m are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom. Its mean is m, and its variance is 2m.

Here is a graph of the Chi-Squared distribution 7 degrees of freedom.

Problem

Find the 95^th percentile of the Chi-Squared distribution with 7 degrees of freedom.

Solution

We apply the quantile function qchisq of the Chi-Squared distribution against the decimal values 0.95.

Answer

The 95^th percentile of the Chi-Squared distribution with 7 degrees of freedom is 14.067.