QUESTION FOUR [25] The data gathered {optimistic (a); most probable (m) and pessimistic (b) times} for a project you are managing are listed in the table below:

4.1 Using the PERT formula, calculate the time and the variance for each activity. (5) 4.2 Construct the network (AON) and identify the critical path (12) 4.3 Calculate the probability of this project finishing within: (8) 48 days 50 days

\begin{tabular}{|c|c|c|c|c|} \hline Activity & Predecessor & MostOptimistic(a) & MostProbable(m) & MostPessimistic(b) \\ \hline & & \multicolumn{3}{|c|}{ Days } \\ \hline A & - & 7 & 8 & 12 \\ \hline B & - & 3 & 6 & 9 \\ \hline C & - & 4 & 7 & 11 \\ \hline D & A;B & 8 & 12 & 16 \\ \hline E & B;C & 5 & 6 & 7 \\ \hline F & D & 9 & 13 & 16 \\ \hline G & E & 6 & 8 & 13 \\ \hline H & F;G & 4 & 9 & 14 \\ \hline I & H & 3 & 5 & 6 \\ \hline \end{tabular}