$($a$)$ A certain project takes $40$ days along the critical path and has a variance of $9$ days. Compute the expected completion time for the project with the following probabilities:

$($i$)94\mathrm{.}5\%$

$($ii$)46\%$

$($iii$)75\%$

$\backslash$table$[[$Normal variate,Probabilities$],[0\mathrm{.}5,0\mathrm{.}308],[0\mathrm{.}1,0\mathrm{.}46],[0,0\mathrm{.}5],[1,0\mathrm{.}841],[0\mathrm{.}69,0\mathrm{.}75],[1\mathrm{.}6,0\mathrm{.}945]]$