Student t Distribution

Assume that a random variable Z has the standard normal distribution, and another random variable V has the Chi-Squared distribution with m degrees of freedom. Assume further that Z and V are independent, then the following quantity follows a Student t distribution with m degrees of freedom.

Here is a graph of the Student t distribution with 5 degrees of freedom.

Problem

Find the 2.5^th and 97.5^th percentiles of the Student t distribution with 5 degrees of freedom.

Solution

We apply the quantile function qt of the Student t distribution against the decimal values 0.025 and 0.975.

Answer

The 2.5^th and 97.5^th percentiles of the Student t distribution with 5 degrees of freedom are -2.5706 and 2.5706 respectively.