Control charts for X $$ and S are maintained on a process. After $25$ preliminary subgroups each of size $3$ are evaluated, you have the following data:

$\_($i$=1)^25$x $\_$i$=55\mathrm{.}45$; $\_($i$=1)^25$S$\_$i $=28\mathrm{.}67$

Assume that the process exhibits statistical control and that the quality characteristic is normally distributed with specifications at $2\mathrm{.}25\backslash$pm $4.$

Estimate the capability ratios Cp$,$ Cpk$,$ Cpkm and Cpm$.$ Interpret these ratios.

How much improvement can be achieved by centering the process?