Consider the following information about a probabilistic project:

Activity Immediate Predecessors Time $($weeks$)$

Optimistic Likely Pessimistic

A $138$

B A $2711$

C A $4610$

D B $3715$

E C $51016$

F D$,$ E $3615$

G F $4712$

a$.$ Calculate the expected durations and the variance $($or standard deviation$)$ for each activity.

b$.$ What is the expected project completion time and the project standard deviation?

c$.$ What is the likelihood the project will be finished by week $38?$

d$.$ If you wanted to be $99\%$ confident of delivering the project on time, how much additional time would you need to add to the schedule?