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

a) Calculate mean duration and standard deviation for all the activities using the beta distribution. [4pts] 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? [30 pts ] c) What is the 92% confidence interval for the length of the critical path? [4 pts] 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. [4 pts] e) Calculate the probability of completing the project between 35 and 40 weeks? [4 pts] f) Answer the project managers question: I want to tell the client that there is a 10.03% chance the project will take longer than X weeks _{- what figure should I give them (i.e. find X)? [4]}

(please show work step by step and excel file)