Problem #$5(2$ pts$)$: For a stable process with USL$=47$ and LSL$=43,$ control charts for and R are used to monitor the process. After $20$ samples of size $5$ are analyzed, we found that:

and

We frequently use the equation $\backslash$sigma $=$R $$d$\_2$ to estimate the process standard deviation. In this case, d$\_2=2\mathrm{.}326$ when n$=5.$ Calculate and comment on Cp and Cpk of this process.

Based on the following equation, calculate the $95\%$ confidence interval for C$\_$p$,$ i$.$e$.,\backslash$alpha $=5\%$