Question

Use the following activities and their three duration estimates (in days) to do the following

1. Calculate the probability that the project will take at least 19 days - use 2 decimals when determining the duration

1. determining the duration

Path	Activity	Optimistic	Most Likely	Pessimistic
a-b-c	A	4	5	6
	B	7	8	10
	C	3	5	9
d-e-f	D	7	8	11
	E	2	3	4
	f	1	4	6

Answer 1

Expected Duration of Activity = (Optimistic Time + 4*Most Likely Time + Pessimistic Time)/6

Expected Duration of Activity A = (4+4*5+6)/6 = 5 days

Expected Duration of Activity B = (7+4*8+10)/6 = 8.17 days

Expected Duration of Activity C = (3+4*5+9)/6 = 5.33 days

Expected Duration of Path A-B-C = 5+8.17+5.33 = 18.50 days

Expected Duration of Activity D = (7+4*8+11)/6 = 8.33 days

Expected Duration of Activity E = (2+4*3+4)/6 = 3 days

Expected Duration of Activity F = (1+4*4+6)/6 = 3.83 days

Expected Duration of Path D-E-F = 8.33+3+3.83 = 15.16 days

From above,

Critical Path = A-B-C

Variance = ((Pessimistic Time - Optimistic Time)/6)^2

Varince of A = ((6-4)/6)^2 = 0.11

Varince of B = ((10-7)/6)^2 = 0.25

Varince of C = ((9-3)/6)^2 = 1.00

Total Variance = 1.36

SD = Variance^(1/2)

SD = (1.36)^(1/2) = 1.166 = 1.17

Expected Duration = 18.50

Z = (X-Mean)/SD

Z = (19-18.50)/1.17

Z = 0.4274

Probability = NORM.S.DIST(0.4274,1)

Probability = 0.6655 = 66.55%