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$.$

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

Activity Optimistic Time Most Likely Time Pessimistic Time

A $7914$

B $228$

C $81216$

D $3510$

E $468$

F $6810$

G $234$

H $228$

I $6816$

J $4614$

K $225$