Consider the network described in the table below. Activity J K L M N o Immediate Predecessor(s) Pessimistic 19 9 J 10 J 3 KM 9 KM 10 LN 12 Optimistic 4 7 5 3 1 4 3 Probable 10 8 6 3 5 7 8 a. Draw the network diagram and fill out the chart below (by doing the forward and backward path analysis). (8 pts) Late Early Start Early Finish Late Start Slack Time Finish Expected Task Time Variance J K L M OZ- P b. Write the critical path and calculate the expected duration and standard variance of the critical path. (4 pts) c. 1) Calculate the probability that the project will be completed in fewer than 30 time units. 2) How much time does it need to finish the project by 95% chance? (4pts) d. Draw the Gantt Chart for this problem. (4pts)