Question

Consider the office renovation project data in the following table. A "zero" time estimate means that the activity could take a very small amount of time and should be treated as a numeric zero in the analysis.

a. Based on the critical path, find the probability of completing the office renovation project by 38 days. Refer to the standard normal table. (Make sure to round all intermediate calculations for te and variance to two decimal places.)

	Time Estimates (days)
Activity	Optimistic	Most Likely	Pessimisitic	Immediate Predecessor(s)
START	0	0	0
A	5	10	15	START
B	0	1	3	A
C	15	20	32	A
D	3	5	8	B
E	2	3	4	D
F	8	10	13	C
G	0	2	3	D
H	1	2	4	G
I	2	2	2	C, G
J	2	3	5	I
K	0	1	2	H
L	1	2	3	J, K
FINISH	0	0	0	E, F, L

Answer 1

The critical path is A-C-F

Expected time for the activity A = (5 + 4*10 + 15)/6 = 10

Expected time for the activity C = (15 + 4*20 +32)/6 = 21.16

Expected time for the activity F = (8 + 4*10 + 13)/6 = 10.16

Total estimated time of completion = 10 + 21 + 10 = 41.32 days

Variance for event A = ((15 - 5)/6)² = 2.7889

Variance for event C = ((8 - 3)/6)² = 0.6938

Variance for event F = ((13 - 8)/6)² = 0.6938

Total variance = 2.7889 + 0.6938 + 0.6938 = 4.1765

Standard deviation = $\sqrt{}$ 4.1765 = 2.0436

z-score = (38 - 41.32) / 2.0436 = -1.624

Probability (z< -1.624) = 0.0526

Hence, probability of completing the office renovation project by 38 days is 5.26%