an important question in project scheduling is identifying the probability of completing the project within a particular duration of time. many software parkages and operations text advocate making such probablity calcutions by focusing on thr variabilty of activity time for activities on the critical path. specifically, the uncertain in project completion can be described via normal probabilty distribution with mean equal to the sum of the mean activity times along the critical path and standard deviation equal to square root of the sum of the variances along the critical path.

recall the dragon fly UAV project addressed in class, where the critical path identified as the sequence of activity A1-A2-A4-A5-A8-A9-A10. Assume uncertainty in activity times can be described via normal probability distribution with means and standard deviations given below. this, using the method described above, project completion time might be modeled via a normal distribution with a mean of 57 days and standard deviation of 11.76 days.

activity A1 A2 A3 A4 A5 A6 A7 A8 A9 A10

Mean 9 3 11 7 8 6 21 10 15 5

St.Dev 4.5 1.5 5.5 3.5 4 3 10.5 5 7.5 2.5

Question. Using the technique described above, calculate the probabilty of completing the UAV project proposal in 70 days or less