A sample of $28$ commuters in Chicago showed the average of the commuting times was $32\mathrm{.}8$ minutes.

If the standard deviation was $7\mathrm{.}1$ minutes, find the following:

a$.$ Find the $95\%$ lower confidence interval of the true mean.

b$.$ The $t_{\frac{}{2}}$ at $95\%$ confidence level is equal to: