Thefollowing table shows the activities needed to complete a project along with precedences and activity durations (in weeks). The precedence column (headed "Follows") shows which activities must be completed before given activity can begin.

Activity	Follows	Optimistic Duration	Most Likely Duration	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

a) Calculate mean duration and standard deviation for all the activities using the beta distribution. b) Construct a network diagram for this problem using the mean durations calculated in part (a), calculate the LS(Foll.), ES(Prec.) and total float for all the activities, and hence identify the critical path.What is the mean completion time for the project? What is the standard deviation of the critical path? c) What is the 92% confidence interval for the length of the critical path?

d) Assuming the probability distribution of the length of the critical path can be approximated by a normal distribution with the mean and standard deviation calculated in part (b), calculate the probability of completing the project within 42 weeks. e) Calculate the probability of completing the project between 35 and 40 weeks? f) If there is10.03% chance the project will take longer than X weeks_{- what figure should I give them (i.e. find X)?" [4]}