Question

activity	preceding	optimistic	probability	pessimistic
a	--	7	9	14
b	a	2	2	8
c	a	8	12	16
d	a	3	5	10
e	b	4	6	8
f	b	6	8	10
g	c,f	2	3	4
h	d	2	2	8
i	h	6	8	16
j	g,i	4	6	14
k	e,j	2	2	5

a. What is the estimated time of completing the project if the critical path is A-D-H-I-J-K?

b. calculate the project variance?

c. Compute the project standard deviation?

d. Find the probability that the project will be completed in less than the project completion time?

Answer 1

Answer:

Activity	Optimistic time-a	Expected completion time-m	Pessimistic time-b	Expected time= (a+4*m+ b)/6	Variance, (sigma)^2= (b-a/6)^2
A	7	9	14	9.50	1.36
B	2	2	8	3.00	1.00
C	8	12	16	12.00	1.78
D	3	5	10	5.50	1.36
E	4	6	8	6.00	0.44
F	6	8	10	8.00	0.44
G	2	3	4	3.00	0.11
H	2	2	8	3.00	1.00
I	6	8	16	9.00	2.78
J	4	6	14	7.00	2.78
K	2	2	5	2.50	0.25

Answer a:	the project is expected to take 36.50 days along critical path ADHIJK
Answer b:	total project variance= 9.53 (sum of the variance of activities on critical path)
Answer c:	standard deviation= sqrt(variance)= sqrt(9.53)= 3.08
step 1	we will find the variance of the tasks which lie on critical path ADHIJK
step 2	mean project time (u) of the critical path is=				36.50
step 3	Required completion time is 36.5 weeks
step 4	standard deviation= sqrt(variance)= sqrt(9.53)=				3.087
step 5	because Z= (given completion time- u)/standard deviation=				0
step 6	P(z<0)=			0.5000	50.00%
Answer d:	probability= 50%