A services process is monitored using $\stackrel{}{x}$ and $R$ charts. Eight samples of $n=10$ observations have been gathered with the following results:

$\backslash$table$[[$Sample$,$Mean,Range$],[1,4\mathrm{.}2,\mathrm{.}43],[2,4\mathrm{.}4,\mathrm{.}52],[3,3\mathrm{.}6,\mathrm{.}53],[4,3\mathrm{.}8,\mathrm{.}20],[5,4\mathrm{.}9,\mathrm{.}36],[6,3\mathrm{.}0,\mathrm{.}42],[7,4\mathrm{.}2,\mathrm{.}35],[8,3\mathrm{.}2,\mathrm{.}42]]$

a$.$ Using the data in the table, compute the center line, the upper control limit$,$ and the lower control limit for the $\stackrel{}{x}$ and $R$ charts.

b$.$ Is the process in control? Interpret the charts.

c$.$ If the next sample results in the following values $(2\mathrm{.}5,5\mathrm{.}5,4\mathrm{.}6,3\mathrm{.}2,4\mathrm{.}6,3\mathrm{.}2,4\mathrm{.}0,4\mathrm{.}0,3\mathrm{.}6,4\mathrm{.}2),$ will the process be in control?