a) Calculate mean duration and standard deviation for all theactivities using the beta distribution. [4pts]
  
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 ]
  
c) What is the 92% confidence interval for the length of thecritical path? [4 pts]
  
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]
  
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)?”[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