Solution

The Process Capability Index $($Cpk$)$ is a measure of the ability of a process to produce products within specification limits$.$ It is calculated as the minimum of two values: $[$Cpk $=$ min$[($USL $-\backslash$mu $)/(3*\backslash$sigma $),(\backslash$mu $-$ LSL$)/(3*\backslash$sigma $)]],$ where USL and LSL are the upper and lower specification limits$,\backslash$mu is the average pressure, and $\backslash$sigma is the standard deviation of the pressure.

In this case, the USL and LSL are $70$ PSI and $55$ PSI, respectively, the average pressure is $59$ PSI, and the standard deviation is $2$ PSI.

Therefore, the Process Capability Index $($Cpk$)$ is$[$Cpk $=$ min$[(59-55)/(3*2),(55-59)/(3*2)]]$

$[$Cpk $=$ min$[0\mathrm{.}10,-0\mathrm{.}13]]$

Final answer: The Process Capability Index $($Cpk$)$ is $0\mathrm{.}10.$