EK Chemical Company sells a specialty chemical in packages marked $114$ g$.$ In$$ reality, EK has set the process mean at $115$g$,$ and the process currently has a standard deviation of $2\mathrm{.}25$ g$.$ Suppose the customer will accept anywhere from $111$ to $117$g$,$ as long as the average package has at least g$.$

Part $2$

a$.$ The process capability index for the current manufacturing process is

$$

$0\mathrm{.}296.($Enter your response rounded to three decimal$$ places.$)$

Part $3$

The process

is not

capable of meeting the tolerance limits$99\mathrm{.}7\%$ of the time.

Part $4$

b$.$ Now suppose EK recenters the manufacturing process so that the process mean is exactly $$g$,$ while the standard deviation remains the same.

The process capability ratio is

$$