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 σ^{2}_{cp}= 13.722

Standard deviation = √σ^{2}cp = 3.704

Probability of completing in 68 days: D=68,

Z = (D-µ)/√σ^{2}cp, = (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)/√σ^{2}cp, = (63-66.4)/√3.704 = -0.92

From tables the probability is 17.8%