For the given PERT network, the three time estimates are given along the activity arrows in the figure.

i$.$ Determine the critical path, also determine the probability of completing the job in $20$ days.

ii$.$ What project duration will have $95\%$ confidence of completion.

The values of Z and corresponding probability are given in the following table:

$\backslash$table$[[Z,1\mathrm{.}0,1\mathrm{.}1,1\mathrm{.}2,1\mathrm{.}5,2\mathrm{.}0,3\mathrm{.}0],[$Probability$,84\mathrm{.}13,86\mathrm{.}43,88\mathrm{.}9,93\mathrm{.}92,97\mathrm{.}92,99\mathrm{.}87]]$