A controlled process exhibits an overall average of $x-$bar$-$bar $=2\mathrm{.}5$ and $r-$bar $=0\mathrm{.}42.$ Samples of six items were taken from the process.

a$.$ What is the mean process capability $($round to $3$ decimals$)?$

$UC{L}_{x\frac{-}{b}ar}=$

$LC{L}_{x-\text{b}\text{a}\text{r}}=$

b$.$ Can this process consistently produce a part with the following customer specifications: $2\mathrm{.}50+-0\mathrm{.}25?$ Demonstrate and explain why or why not, do not just answer yes or no$.$

Process is $$ of meeting the customer's specifications. $($answer options: capable or not capable$)$

Why: $($answer options: both specs are inside the control limits; both specs are outside the control limits; one spec is inside and one spec is outside the control limits$)$

c$.$ If the customer's part specifications are $2\mathrm{.}50+-0\mathrm{.}15,$ can this process consistently product the part? Demonstrate and explain why or why not, do not just answer yes or no$.$

Process is $$ of meeting the customer'spsecifications. $($answer options: capable or not capable$)$

Why? $($answer options: both specs are inside the control limits; both specs are outside the control limits; one spec is inside and one spec is outside the control limits$)$