Data Regarding the Activities for a Project Are Presented Below

Data regarding the activities for a project are presented below. The times are in weeks. The critical path for this project is A-D-H-I-J-K. $\begin{array}{|c|c|c|c|}\hline\text { Activity } & \text { Optimistic Time } & \text { Most Likely Time } & \text { Pessimistic Time } \\\hline \text { A } & 7 & 9 & 14 \\\hline \text { B } & 2 & 2 & 8 \\\hline \text { C } & 8 & 12 & 16 \\\hline \text { D } & 3 & 5 & 10 \\\hline \text { E } & 4 & 6 & 8 \\\hline \mathrm{F} & 6 & 8 & 10 \\\hline \mathrm{G} & 2 & 3 & 4 \\\hline \mathrm{H} & 2 & 2 & 8 \\\hline \mathrm{I} & 6 & 8 & 16 \\\hline \mathrm{J} & 4 & 6 & 14 \\\hline \mathrm{K} & 2 & 2 & 5 \\\hline\end{array}$
a.Determine the standard deviation of the critical path.
b.Determine the probability of completing the project in 38 weeks or less.
c.What is the probability of completing the project in 32 weeks or less?