$(20$ points$)$ A high voltage power supply should have a normal output voltage of $350V.$ A

sample of four units is selected each day and tested for process$-$control purposes. The data shown

below give the difference between the observed reading on each unit and the normal voltage

times the; that is$,$ observed voltage on unit $i-350.$

Note that an Excel datasheet can be found on Moodle.

$($a$)$ Show calculations of the center line, the UCL and the LCL by hand using Table $4\mathrm{.}2.$

$($b$)$ Find the center line, the UCL, the LCL by Excel and plot the R chart and the $\stackrel{}{x}$ chart.

$($c$)$ Did the process appear to be in control based on the charts created?

$($d$)$ If specifications are at $350V\frac{+}{-}5V,$ find the percentage of conforming power supplies

produced by this process. Assume the voltage is normally distributed.