Here are summary statistics for randomly selected weights of newborn girls: $n=36,\stackrel{}{x}=3197\mathrm{.}2g,s=692\mathrm{.}6g.$ Use a confidence level of $95\%$ to complete parts $($a$)$ through $($d$)$ below.

a$.$ Identify the critical value $t_{\frac{}{2}}$ used for finding the margin of error.

$t_{\frac{}{2}}=2\mathrm{.}030$

$($Round to two decimal places as needed.$)$

b$.$ Find the margin of error:

$E=234\mathrm{.}39$

$($Round to one decimal place as needed.$)$

c$.$ Find the confidence interval estimate of $.$

$($Round to one deci mal place as needed$)$