You will first determine the activity durations and the variance for each task. The answer is here. table-for-Pert-practice-problem
The basic network diagram is shown here.PERT-Scheduling-practice-solution
From the diagram the expected completion time = 66.4 days. = µ
The critical path is the path connecting tasks 2,3,4,5,7,8,9.
Variance of critical path activities σ2cp= 13.722
Standard deviation = √σ2cp = 3.704
Probability of completing in 68 days: D=68,
Z = (D-µ)/√σ2cp, = (68-66.4)/√3.704 = 0.43; From the normal distribution table, the probability is 66.6%.
Probability for 63 days: D=63
Z = (D-µ)/√σ2cp, = (63-66.4)/√3.704 = -0.92
From tables the probability is 17.8%