You are provided with the following information for a project, with activity durations given in days:

Activity	Immediate Predecessor	Optimistic Time (a)	Most Likely Time (m)	Pessimistic Time (b)
A	---	3	5	8
B	---	2	4	7
C	---	6	8	11
D	A, B	5	7	9
E	B, C	3	6	10
F	C	4	5	6
G	E, F	7	10	12
H	D	2	3	4
I	E, G, H	10	13	16
J	G, I, F	12	15	17
K	H	8	11	14

1. Construct a project network.
2. Determine the expected times and variances for each activity.
3. Determine the critical path after you have found ES, EF, LS, LF and Slack. State the path and time the project is expected to take.
4. What is the probability that the project would be completed within 50 days?
5. What is the probability that the project would be completed within 54 days?