Question

activity	follows	optimistic duration	most likely direction	pessimistic duration
A	-	4	6	14
B	A,C	3	4	5
C	-	3	5	13
D	A,E	12	18	24
E	-	8	10	18
F	A,E	4	6	8
G	B,F	7	8	9
H	G	10	12	14
I	G	5	6	7
J	D,I	5	7	9

Calculate the probability of completing the project between 35 and 40 weeks? [4 pts]
  
f Answer the project manager’s question: “I want to tell the client that there is a 10.03% chance the project will take longer than X weeks _{- what figure should I give them (i.e. find X)?” [4]}

Answer 1

We need to calcuate the project duration using the critical path method / PERT. The expected duration is

E = (optimistic + 4*most likely + pessimistic) / 6

Variance = ((pessimistic - optimistic)/6)^2

The calculated values are shown below

The exxpected duration is 38 weeks and the variance for this duration is 3.88 weeks.

The z value for less 35 weeks = (35-38)/sqrt(3.88) = -1.52

The corresponding probability = 0.063

The z value for less than 40 weeks = (40-38)/sqrt(3.88) = 1.01

The corresponding probability = 0.845

The range between 35 to 40 weeks = 0.845-0.063 = 0.782

The probability of finishing between 35 and 40 weeks is 0.782

A 10.03% probability means that the z value is -1.27

This means -1.27 = (X-38)/sqrt(3.88) or X = 35.47 weeks