CPM and PERT in Construction Questions and Answers

Q: The probability distribution taken to represent completion time in PERT analysis is:

PERT represents activity completion time by a Beta distribution.PERT assumes each activity time follows a beta distribution, which is bounded by the optimistic and pessimistic times and can be skewed either way. That assumption is what gives the formulas te = (to + 4tm + tp)/6 and σ = (tp - to)/6.The normal distribution is the trap: it is used for the project completion time, which by the central limit theorem is roughly normal when many activities are added, not for a single activity. Gamma and log-normal are not the PERT assumption.

The critical path method is a/an ______ oriented technique, which is used in project management.

A.activity
B.event
C.time
D.resource

Exam Year(s)

DSSSB JE - 2023,

Answer: A

The critical path method (CPM) is an activity-oriented technique: the network is drawn with arrows representing the activities, and the critical path is the longest chain of activities. PERT, in contrast, is an event-oriented technique, in which the nodes are events and the times are probabilistic. CPM is not oriented to time or to resource as such, although it gives time results (the project duration and the float), and resource levelling is a later step.

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The optimistic time, most likely time and pessimistic time estimates of an activity are 5, 10 and 21 days respectively. What are the expected time and standard deviation?

A.12, 3.67
B.11, 2.67
C.11, 4.67
D.10, 16.27

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: B

The expected time is 11 days and the standard deviation 2.67 days: 11, 2.67.

PERT uses the beta-distribution estimates:

\[ \begin{aligned} t_e &= \frac{t_o + 4t_m + t_p}{6} = \frac{5 + 40 + 21}{6} = 11 \\ \sigma &= \frac{t_p - t_o}{6} = \frac{21 - 5}{6} = 2.67 \end{aligned} \]

The variance would be \(2.67^2 = 7.1\). 12, 3.67 and 11, 4.67 misplace the arithmetic, and 10, 16.27 takes the most likely time as the expected time.

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The probability distribution taken to represent completion time in PERT analysis is:

A.Gamma distribution
B.Normal distribution
C.Beta distribution
D.Log-normal distribution

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: C

PERT represents activity completion time by a Beta distribution.

PERT assumes each activity time follows a beta distribution, which is bounded by the optimistic and pessimistic times and can be skewed either way. That assumption is what gives the formulas t_e = (t_o + 4t_m + t_p)/6 and σ = (t_p - t_o)/6.

The normal distribution is the trap: it is used for the project completion time, which by the central limit theorem is roughly normal when many activities are added, not for a single activity. Gamma and log-normal are not the PERT assumption.

Discuss in Forum

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CPM and PERT in Construction Questions and Answers

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