A Company Wants to Develop a Project Using PERT to Modify

A company wants to develop a project using PERT to modify one of their products which has poor sales. They have determined the following activities, precedence relationships and time estimates in days for the project:
$$\begin{array} { c c c c c } & \text { Immediate } & \text { Optiristic } & \text { Most Likely } & \text { Pessimistic } \\\text { Activity } & \text { Predecessors } & \text { t }_o & \text { t }_m & \text { t }_p \\\hline \text { a } & \text { mone } & 4 & 6 & 7 \\\text { b } & \text { a } & 1 & 2 & 3 \\\text { c } & \text { a } & 5 & 5 & 5 \\\text { d } & \text { b } & 7 & 9 & 12 \\\text { E } & \text { b } & 2 & 4 & 8 \\\text { f } & \text { c, d } & 6 & 9 & 10\end{array}$$
a. What is the expected duration for activity a?
b. What is the variance for activity d?
c. How many paths are there in the network?
d. What is the earliest start ES) time for activity e?
e. What is the slack in days for activity b?f. What is the critical path
g. What is the duration of the critical path in days
h. What is the standard deviation of the critical path
i. What is the probability that the project will take longer than 28 weeks to complete?