Consider the activities, durations, and predecessor relationships in the following network. Draw the Network Diagram.

Activity Description

Immediate

Predecessor$($s$)$

Optimistic

$($Weeks$)$

Most Likely

$($Weeks$)$

Pessimistic

$($Weeks$)$

A

$---$

$4$

$7$

$10$

B

A

$2$

$8$

$20$

C

A

$8$

$12$

$16$

D

B

$1$

$2$

$3$

E

D$,$ C

$6$

$8$

$22$

F

C

$2$

$3$

$4$

G

F

$2$

$2$

$2$

H

F

$6$

$8$

$10$

I

E$,$ G$,$ H

$4$

$8$

$12$

J

I

$1$

$2$

$3$

a$.$ What is the expected time for activity B$?$

b$.$ What is the variance for activity B$?$

c$.$ Based on the calculation of estimated times, what is the critical path?

d$.$ What is the estimated time of the critical path?

e$.$ What is the activity variance along the critical path?

f$.$ What is the probability of completion of the project before week $42?$