a) Calculate mean duration and standard deviation for all theactivities using the beta distribution. [4pts]
 Â
b) Construct a network diagram for this problem using the meandurations calculated in part (a), calculate the LS(Foll.),ES(Prec.) and total float for all the activities, and henceidentify the critical path . What is the mean completion time forthe project? What is the standard deviation of the critical path?[30 pts ]
 Â
c) What is the 92% confidence interval for the length of thecritical path? [4 pts]
 Â
d) Assuming the probability distribution of the length of thecritical path can be approximated by a normal distribution with themean and standard deviation calculated in part (b), calculate theprobability of completing the project within 42 weeks. [4pts]
e) Calculate the probability of completing the project between 35and 40 weeks? [4 pts]
 Â
f) Answer the project manager’s question: “I want to tell theclient that there is a 10.03% chance the project will take longerthan X weeks - what figure should I give them (i.e. find X)?â€[4]
(please show work step by step and excel file)
activity | follows | optimistic duration | most likely direction | pessimistic duration |
A | - | 4 | 6 | 14 |
B | A,C | 3 | 4 | 5 |
C | - | 3 | 5 | 13 |
D | A,E | 12 | 18 | 24 |
E | - | 8 | 10 | 18 |
F | A,E | 4 | 6 | 8 |
G | B,F | 7 | 8 | 9 |
H | G | 10 | 12 | 14 |
I | G | 5 | 6 | 7 |
J | D,I | 5 | 7 | 9 |
