BlueBolt Bottlers has a bottle$-$filling process with a mean value of $54$ ounces and a standard deviation of $5\mathrm{.}5$ ounces.

a$.$ Suppose that the upper and lower tolerance limits are $59$ and $49$ ounces, respectively.

The process capability ratio is $.($Enter your response rounded to three decimal places.$)$

b$.$ Now suppose BlueBolt Bottlers makes some process improvements, thereby lowering the standard deviation of the process to $2\mathrm{.}0$ ounces, rather than $5\mathrm{.}5$ ounces.

The process capability ratio is $($Enter your response rounded to three decimal places.$)$

The improved BlueBolt process able to meet the tolerance limits $99\mathrm{.}7\%$ of the time.

This enough for BlueBolt Bottlers to achieve Six Sigma quality levels.