Samples of n $=6$ items each are taken from a process at regular intervals. A quality characteristic is measured, and x $$ and R values are calculated for each sample. After $50$ samples, we have $\_($i$=1)^50($x$\_$i $)=2,500$ and $\_($i$=1)^50$R$\_$i$=250.$ Assume that the quality characteristic is normally distributed.

Compute control limits for the x $$ and R control charts. $(5)$

All points on both control charts fall between the control limits computed in part $($a$).$ What are the natural tolerance limits of the process? $(5)$

If the specification limits are $52\backslash$pm $5\mathrm{.}0,$ what are your conclusions regarding the ability of the process to produce items within these specifications? $(5)$

Assuming that if an item exceeds the upper specification limit it can be reworked, and if it is below the lower specification, it must be scrapped, what percentage scrap and rework is the process producing? $(5)$