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

$1\mathrm{.}21\mathrm{.}2$

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

$0\mathrm{.}190\mathrm{.}19$

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

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

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

$0\mathrm{.}70\mathrm{.}7$

kg and

$1\mathrm{.}91\mathrm{.}9$

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

Part $3$

Tyler Apiaries

$$

$$

is not

is

capable of meeting the tolerance limits$99\mathrm{.}7\%$ of the time.