Question

Consider the following work breakdown structure: What is the probability of finishing the project at exactly 201 days?

		Time Estimates (days)
Activity	Precedes	Optimistic			Most Likely			Pessimistic
Start	A,B		-			-			-
A	C,D		44			50			56
B	D		45			60			75
C	E		42			45			48
D	F		31			40			49
E	F		27			36			39
F	End		58			70			82

		1.
		0.
		0.9.
		0.6.
		2.5.

Answer 1

Answer: 0.6

Explanation:

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	44	50	56	50.00	4.00
B	45	60	75	60.00	25.00
C	42	45	48	45.00	1.00
D	31	40	49	40.00	9.00
E	27	36	39	35.00	4.00
F	58	70	82	70.00	16.00

Paths

Paths	Duration	Variance
ACEF	200.00	25.00
ADF	160.00
BDF	170.00

ACEF is the longest path (critical path) with a variance of 25

to find the probability for 201 days

step 1	we will find the variance of the tasks which lie on critical path				25.00
step 2	mean project time (u) of critical path is=				200
step 3	Required completion time is				201 days
step 4	standard deviation= sqrt(variance)=				5.000
step 5	because Z= (given completion time- u)/standard deviation				0.200
step 6	P(z)= using NORM.S.DIST(z,true)				0.5793 ~0.6