Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths $(mm)$ of skulls from $150$ A$.$D$.$ Construct a $95\%$ confidence interval estimate of the mean skull width.

$127\mathrm{.}7,137\mathrm{.}6,125\mathrm{.}8,132\mathrm{.}3,142\mathrm{.}9,134\mathrm{.}8,139\mathrm{.}1,129\mathrm{.}1$

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