Prohlem $3(50$ Points$)$: Consider the PERT network, as shown below. The duration estimate for each activity is given in the notation $0-m-p,$ where: $0-$optimistic, $m-$most likely $($mode$),$ p $-$pessimistic. The estimate times are given in weeks. What is the probability that this project will be completed in $81$ weeks?

Note: For project daration. calculate the longest path:

$,t_e=\frac{t_0+4t_m+t_p}{6}$

variance $=(\frac{t_p+t_0}{6}{)}^2$

$EF=ES+t_e$

$LS=LF+t_e$

$TF=LS-ES$