Question

Statement (I): In a multipath PERT network, the project duration resulting from the critical path always has a 50% probability of completion by that duration.

Statement (II): The expected - path duration together with 3-times the standard deviation of that expected duration must be considered for all the paths in the network. 

1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true

Answer 1

Correct Answer - Option 3 : Statement (I) is true but Statement (II) is false

Statement I: True

The probability of completion of project for any time say T_s is decided by a factor called probability density function and it is given as:

\(Z = \frac{{{T_S} - {T_E}}}{\sigma }\)

Where,

σ is the standard deviation

T_s is the scheduled completion of project

T_E is the expected completion time

The relation between Z and probability of completion of work is given as:

Z values	-3	-2	-1	0	1	2	3
P Values (%)	0.13	2.28	15.67	50	84.13	97.72	99.87

It is clear from the above table that If T_s = T_E i.e. the project duration resulting from the critical path always has a 50% probability of completion by that duration.

Statement II: False

PERT is based on the probabilistic approach and in this three-time estimates namely – Optimistic time (T_o), Pessimistic time (T_p), and most likely time (T_L) is considered for each activity in the path.

The expected or average duration (T_E) of each activity is the weighted average of these three-time durations.  This  T_E and standard deviation σ are considered together for each activity in the path network.