Question $7,$ Problem $29$

HW Score: $51\mathrm{.}67\%,31$ of $60$

Part $1$ of $2$

points

Points: $3$ of $12$

Canine Gourmet Super Breath dog treats are sold in boxes labeled with a net weight of $12$ ounces $(340$ grams$)$ per box. Each box contains $8$ individual $1\mathrm{.}5-$ounce packets. To reduce the chances of shorting the customer, product design specifications call for the packet$-$filling process average to be set at $44\mathrm{.}0$ grams so that the average net weight per box of $8$ packets will be $352$ grams. Tolerances are set for the box to weigh $352+-13$ grams. The standard deviation for the packet$-$filling process is $1\mathrm{.}01$ grams. The target process capability ratio is $1\mathrm{.}33.$ One day, the packet$-$filling process average weight drifts down to $43\mathrm{.}5$ grams. Is the packaging process capable? Is an adjustment needed?

Since the process capability index, $C_{pk},$ is $,$ the process is not capable $($ Enter your response rounded to three decimal places.$)$