$1.$When using the process potential equation, a value of $1\mathrm{.}0$ has been chosen

somewhat arbitrarily as the threshold for high quality manufacturing. As manufacturing becomes increasingly competitive and quality expectations increase, many companies feel this threshold is inadequate. Rather than redefining the process potential equation one can simply choose a different threshold to denote high quality manufacturing.

Compute the process potential threshold needed if high quality production is defined as eing within plus$/$minus $5$ standard deviations around the target. $($You must show work.$)$