Consider the network described in the table below.

Activity	Immediate Predecessor(s)	Pessimistic	Optimistic	Probable
J	--	15	8	10
K	--	9	7	8
L	J	10	5	6
M	J	3	3	3
N	K, M	9	1	5
O	K, M	11	3	7
P	L, N	11	2	8

1. Draw the network diagram and fill out the chart below (by doing the forward and backward path analysis).

Task	Expected Time	Variance	Early Start	Early Finish	Late Start	Late Finish	Slack Time
J
K
L
M
N
O
P

2. Write the critical path and calculate the expected duration and standard variance of the critical path.

3. a. Calculate the probability that the project will be completed in fewer than 30 time units.

b. How much time does it need to finish the project by 90% chance?

4. Draw the Gantt Chart for this problem.