A process is in statistical control with and $.$ The control chart uses a sample size of $.$ Specifications are at $.$ The quality characteristic is normally distributed.

$($a$)$ Estimate the potential capability of the process.

$($b$)$ Estimate the actual process capability.

$($c$)$ How much improvement could be made in process performance if the mean could be centered at the nominal value?

$($c$)$ The capacity of the utility that supplies this company is $61,000$ kWh$.$ What is the probability that demand will not exceed supply by more than $100$ kWh$?$