Example 9.4.5. Similarity between Normal and t-distributions for larger n.
Consider the probabilities \(P(-2 \le Z \le 2)\) vs \(P(-2 \le T \le 2)\) for a t-distribution with r=30 degrees of freedom.
For normal,
\begin{equation*}
P(-2 \le Z \le 2) = \Phi(2) - \Phi(-2) = 0.9545
\end{equation*}
while for t,
\begin{equation*}
P(-2 \le T \le 2) = 0.9454.
\end{equation*}