Many services maintain records of sales noting:A network consists of the following list. Times are given in weeks.

Activity

Preceding

Optimistic

Probable

Pessimistic

A

$--$

$5$

$11$

$14$

B

$-$

$3$

$3$

$9$

C

$--$

$6$

$10$

$14$

D

A$,$ B

$3$

$5$

$7$

E

B

$4$

$6$

$11$

F

C

$6$

$8$

$13$

G

D$,$ E

$2$

$4$

$6$

H

F

$3$

$3$

$9$

a$.$ Draw the network diagram.

b$.$ Calculate the expected duration and variance of each activity.

c$.$ Calculate the expected duration and variance of the critical path.

d$.$ Calculate the probability that the project will be completed in less than $28$ weeks.