A restaurant has large tanks that are cleaned daily. Cleaning includes the use of packaged

detergents, which dissolve in a solution inside the tanks. The company purchases

detergent packages with a fill$-$weight specification of $11\mathrm{.}47+-0\mathrm{.}08$oz$.$ A supplier

representative claims that his company uses statistical process control and will promise an

inherent process capability of $0\mathrm{.}27$ oz for the fill$-$weight specification. The brochure says

nothing else about the process except that the advertised weight of the detergent packages

is $11\mathrm{.}5$ oz $.$

a$.$ Calculate C$\_($pk$)$

b$.$ Should the food processor buy detergent from this supplier? Why or why not?

c$.$ If the supplier had control chart evidence that its fill$-$weight process was in fact

centered a $11\mathrm{.}50$ oz $,$ and was in a state of statistical control, how would your answer

to question $($a$)$ change? Does all output meet specifications?