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Part $1$

Tyler Apiaries sells bees and beekeeping supplies. Bees$($including a$$ queen$)$ are shipped in special packages according to weight. Suppose Tyler changes its processes so that the average package weight is now

$1\mathrm{.}31\mathrm{.}3$

$$kg$,$ with a new standard deviation of

$0\mathrm{.}160\mathrm{.}16$

kg$.$ Tyler markets the packages of bees as weighing

$1\mathrm{.}51\mathrm{.}5$

$$kg$,$ and the lower and upper tolerance limits are

$0\mathrm{.}90\mathrm{.}9$

kg and

$2\mathrm{.}12\mathrm{.}1$

$$kg$,$ respectively. Calculate the process capability index for the weight of the bee packages. Is Tyler able to meet the tolerance$$ limits$?$

Part $2$

The process capability index for the weight of the bee packages is

enter your response here.

$($Enter your response rounded to three decimal$$ places.$)$