Question

Given the information below, what is the probability that the critical path will be completed in 25 weeks?

Time Estimates (Weeks)
Activity	Optimistic	Most Likely	Pessimistic	IP
A	1	4	7	None
B	5	6	7	None
C	2	4	6	B
D	4	16	10	A
E	4	6	14	A, C
F	6	8	16	B
G	1	5	9	D,E,F

The probability is less than 0.25.

The probability is between 0.5 to 0.75.

The probability is between 0.25 5o 0.5.

The probability is more than 0.75.

Answer 1

The calculated values for expected duration, start, stop is shown below.

Activity	Optimistic	Most Likely	Pessimistic	IP	Exp	Var	Start	Finish
A	1	4	7	None	4	1	0	4
B	5	6	7	None	6	0.111111	0	6
C	2	4	6	B	4	0.444444	6	10
D	4	16	10	A	13	1	4	17
E	4	6	14	A, C	7	2.777778	10	17
F	6	8	16	B	9	2.777778	6	15
G	1	5	9	D,E,F	5	1.777778	17	22

The expected project duration is 22 weeks. However there are two critical paths. They have standard deviation of

ADG = 1.94 weeks

BCEG = 2.26 weeks

Using this, the z value for each of the paths are

(25-22)/1.94 = 1.54

(25-22)/2.26 = 1.32

This means their corresponding probabilities are

P(z = 1.54) = 0.9386

P(z= 1.32) = 0.9077

This makes the project completion probability about 90% or higher. This means the correct answer will be

The probability is more than 0.75