Given the Following Activities, Their Durations, and the Predecessor Relationships $\begin{array}{c}\text { Activity } \\\text { Description }\end{array}$

Essay

Given the following activities, their durations, and the predecessor relationships, construct the network flow diagram and answer the questions that follow.

\begin{tabular}{|c|c|c|c|c|}
\hline $\begin{array}{c}\text { Activity } \\\text { Description }\end{array}$ & $\begin{array}{c}\text { Immediate } \\\text { Predecessor(s) }\end{array}$ & $\begin{array}{c}\text { Optimistic } \\\text { (hours) }\end{array}$ & $\begin{array}{c}\text { Most Likely } \\\text { (hours) }\end{array}$ & $\begin{array}{c}\text { Pessimistic } \\\text { (hours) }\end{array}$ \\
\hline $\mathrm{A}$ & - & 7 & 10 & 13 \\
\hline $\mathrm{B}$ & $\mathrm{A}$ & 5 & 11 & 23 \\
\hline $\mathrm{C}$ & $\mathrm{A}$ & 11 & 15 & 19 \\
\hline $\mathrm{D}$ & $\mathrm{B}$ & 4 & 5 & 6 \\
\hline $\mathrm{E}$ & $\mathrm{D}, \mathrm{C}$ & 9 & 11 & 25 \\
\hline $\mathrm{F}$ & $\mathrm{C}$ & 5 & 6 & 7 \\
\hline $\mathrm{G}$ & $\mathrm{F}$ & 5 & 5 & 5 \\
\hline $\mathrm{H}$ & $\mathrm{F}$ & 9 & 11 & 13 \\
\hline $\mathrm{I}$ & $\mathrm{E}, \mathrm{G}, \mathrm{H}$ & 7 & 11 & 15 \\
\hline $\mathrm{J}$ & $\mathrm{I}$ & 4 & 5 & 6 \\
\hline
\end{tabular}

A) What is the expected time for activity E?
B) What is the variance for activity E?
C) What is the critical path based on the calculation of the estimated times?
D) What is the estimated duration of the critical path?
E) What is the estimated variance along the critical path?
F) What is the probability of completion of the project before hour 45?