Please show all formulas and work assosiated

Problem $4)(8$ points$)$

a$)$ A barbecue sauce producer sells their product in a $50$ ounces bottle. Their historical process

mean has been $50$ ounces with a standard deviation of $2\mathrm{.}50$ ounces. If their tolerance limits are set

at $50$ ounces plus or minus $7$ ounces, what is the process capability ratio of the bottle filling

process? $(4$ points$)$

b$)$ A barbecue sauce producer sells their product in a $45$ ounces bottle. Their current process mean

is $45\mathrm{.}5$ ounces with a standard deviation of $1\mathrm{.}15$ ounces. If their tolerance limits are set at $45$ ounces

plus or minus $4$ ounces, what is the process capability index of the bottle filling process? $(4$ points$)$