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 $1\mathrm{.}3$ kg $,$ with a

new standard deviation of $0\mathrm{.}13$ kg $.$ Tyler markets the packages of bees as weighing $1\mathrm{.}2$ kg $,$ and the lower and upper

tolerance limits are $0\mathrm{.}7$ kg and $1\mathrm{.}7$ kg $,$ respectively. Calculate the process capability index for the weight of the bee

packages. Is Tyler able to meet the tolerance limits$?$

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

$($Enter your response rounded to three

decimal places.$)$

Tyler Apiaries

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