The 3-point estimates for a projects tasks, and predecessor relationships are given in the table below.

1. Complete the two empty columns. [5 points]
2. Determine the critical path and all activity slacks. [5 points]
3. What is the expected project duration (T_E)? [5 points]
4. What is the probability of completing the project in 57 periods or less? Provide full analysis. [5 points]
5. What project duration should be negotiated with the customer to expect 90% likelihood of on-schedule delivery? Provide full analysis. [5 points]

ID	Predecessor	to	tm	tp	te	Var
1	None	5	8	17
2	1	3	4	17
3	None	7	11	21
4	1,3	5	6	13
5	3	3	4	11
6	2,4	7	12	23
7	6	11	17	29
8	5,7	2	4	6

Please provide answers for all five parts. Thank you.