Problem $4)(8$ points$)10$

a$)$ A barbecue sauce producer sells their product in a $75$ ounces bottle. Their historical process mean has been $75$ ounces with a standard deviation of $2\mathrm{.}50$ ounces. If their tolerance limits are set at $75$ ounces plus or minus $8$ ounces, what is the process capability ratio of the bottle filling process? $(4$ points$)$

b$)$ A barbecue sauce producer sells their product in a $75$ ounces bottle. Their current process mean is $74$ ounces with a standard deviation of $2\mathrm{.}5$ ounces. If their tolerance limits are set at $75$ ounces plus or minus $8$ ounces, what is the process capability index of the bottle filling process? $(4$ points$)$