A company doing interior design work has been given a new contract to renovate a hotel in Sandton. A list of activities and their optimistic completion time, the most likely completion time, and the pessimist completion time (all in days) for completing the interior design work are given in the table below:

2.1.1 Calculate the expected time and the variance of each project activity and round off your expected times to the nearest number. (12) 2.1.2 Determine the critical path and the expected project completion time. (3) 2.1.3 Calculate the variance of the critical path. (2) 2.1.4 What is the probability that the project will be completed 3 days before the project completion time? (3) 2.1.5 What is the probability that the project will be completed 2 days after the project completion time?

\begin{tabular}{|c|c|c|c|c|} \hline Activity & Immediate & Optimistic Time & Most Likely Time & Pessimistic Time \\ \hline Predecessor & & 10 & 12 & 14 \\ \hline B & & 9 & 10 & 12 \\ \hline C & A & 7 & 9 & 12 \\ \hline D & B, C & 12 & 15 & 17 \\ \hline E & C, D & 6 & 9 & 11 \\ \hline F & C,D,E & 8 & 10 & 13 \\ \hline \end{tabular}