$!$

Required information

The quality$-$control plan for a certain production process involves taking samples of size $4.$ The results from the last $30\mathrm{.}00$ samples can be summarized as follows:

${\displaystyle \underset{i=1}{\overset{30\mathrm{.}00}{}}}{\stackrel{}{x}}_i=712\mathrm{.}5,{\displaystyle \underset{i=1}{\overset{30\mathrm{.}00}{}}}{R}_i=143\mathrm{.}7,{\displaystyle \underset{i=1}{\overset{30\mathrm{.}00}{}}}{s}_i=62\mathrm{.}5$

Compute the $3$ control limits for the $S$ chart. $($Round the final answer to three decimal places.$)$

The LCL is $$

The UCL is $$