The process improvement manager has developed a new machine to cut material for running shoes. The material cannot be more than $+-0\mathrm{.}02$ of an inch from the required thickness of $\mathrm{.}455$ inches. When you took samples $(15$ samples with $10$ observations in each sample$)$ of material cut from the new machine, you calculated the following data: $($note: use $3$ decimal places for calculations$)$

X$-$double bar $=0\mathrm{.}460,R-$bar $=0\mathrm{.}15$

a$)$ What is the upper control limit $($blank $1),$ and what is the lower control limit $($blank

for the $x-$bar chart on this new machine? $($use $3$ decimal places$)$

b$)$ what are the upper $($blank $3)$ and lower $($blank $4)$ control limits for the $R$ chart on this new machine? $($use $3$ decimal places$)$

c$)$ Given the UCL and LCL in part $($a$),$ do you believe the Cpk for the process is $1,>1,$ or please put one of the following answers $($blank $5)$: $1,>1,$ or $<mn\; id="EditorElement\_2540436">1</mn>$

Blank # $1$

A

Blank # $2$

Blank # $3$

Blank # $4$

Blank # $5$