Suppose we are using the CPM with three time estimates $($PERT$)$ to schedule a project. What is the variance of the length of the critical path, if there is a $92\mathrm{.}22\%$ probability that the project will be completed within the expected duration plus three time periods? Select the nearest correct answer. $($HINT: Use the $Z$ formula to find the value$)$

$1\mathrm{.}67$

$2\mathrm{.}34$

$2\mathrm{.}96$

$3\mathrm{.}19$

$4\mathrm{.}46$