A partially solved PERT problem is detailed in the table below. Times are given in weeks.

Activity	Preceding	Optimistic Time	Probable Time	Pessimistic Time	Expected Time	Variance
A	--	7	10	19
B	A	2	2	8
C	A	8	12	16
D	A	3	5	10
E	B	4	6	8
F	B	6	8	10
G	C, F	2	3	4
H	D	2	2	8
I	H	6	8	16
J	G, I	4	6	14
K	E, J	2	5	8

(a) Calculate the expected time and variance for each activity. Enter these values in the appropriate columns in the table above. (b) Which activities form the critical path? (c) What is the estimated time of the critical path? (d) What are the project variance and the project standard deviation?

(e) What is the probability of completion of the project before week 42?