The following table lists the activities needed to complete aproject. The first column lists the activities and the “follows”column shows which other activity or activities, (if any), must becompleted before these activities can start. The remaining columnsgive three estimates of the activity duration; the mean durationcalculated from these estimates and standard deviation assuming abeta distribution of activity duration.

Activity

Follows

Estimates of durations (days) Optimistic Most likely Pessimistic

A	--	3	6	15
B	A	8	14	26
C	A	1	2	9
D	B	2	5	14
E	C	5	7	21
F	D	2	4	12
G	B, E	6	9	18
H	F	1	3	5
I	D, G	2	3	10
J	G	5	7	15

a) Calculate mean duration and standard deviation for allactivities using the beta distribution. (4 points)
  
b) Construct a network diagram for this problem using the meandurations calculated in part (a), calculate the ES (Prec.),LS(Foll.) and the 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?(3 0 points)
  
c) What is the 99% confidence interval for the length of thecritical path? (4 points)
  
d) Assuming that 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 34 days . (4points)
  
e) What is the probability that the project will be completedbetween 38 and 45 days? Show your workings! (4 points)
  
f) Answer the project manager’s question:
“I want to tell the client a project length which I am 89.97% surethat we can meet _- What figure should I give them?\" (4points)