---
title: "CPM vs PERT; te and variance for x, y"
subject: "Project Engineering"
chapter: 3
key: "semester_7/project_engineering:cpm-pert-te-variance-x-y"
source: https://www.bctengineer.com/q/semester_7/project_engineering/cpm-pert-te-variance-x-y
site: BCT Engineering
---

# CPM vs PERT; te and variance for x, y

Project Engineering · Chapter 3: Project Planning and Scheduling

- Asked in: 2066 Bhadra (old course), 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/cpm-pert-te-variance-x-y
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3

## Question

What are the differences between CPM and PERT? Find the te (time estimates) for x and y where to, tm, tp are 4, 6, 8 for x and 3, 5, 6 for y. Also find which is more certain by using S.D. and variance.

## Short answer

CPM uses deterministic single time, while PERT uses three probabilistic times. te = (t_o+4t_m+t_p)/6, σ = (t_p–t_o)/6. For x: te = 6.00, σ = 0.67, variance = 0.44; for y: te = 4.83, σ = 0.50, variance = 0.25. y is more certain because of smaller SD and variance.

## Answer

#### Difference between CPM and PERT

| Basis | CPM | PERT |
|---|---|---|
| Time estimate | One (deterministic) | Three: $t_o, t_m, t_p$ (probabilistic) |
| Nature | Activity oriented | Event oriented |
| Distribution | Not required | Beta distribution assumed |
| Suitable for | Repetitive, known work such as construction | New, research-type, uncertain work |
| Cost | Time-cost trade-off (crashing) is done | Mainly time; cost is not considered |
| Probability of completion | Not computed | Computed using $Z$ value |
| Developed by | Du Pont (1957) | US Navy (1958) |

#### Calculation

$t_e = \dfrac{t_o + 4t_m + t_p}{6}$, $\sigma = \dfrac{t_p - t_o}{6}$, variance $= \sigma^2$.

**For x** ($4, 6, 8$):

$$
\begin{aligned} t_e &= \frac{4 + 24 + 8}{6} = 6.00 \\ \sigma &= \frac{8 - 4}{6} = 0.67, \quad \text{Var} = 0.44 \end{aligned}
$$

**For y** ($3, 5, 6$):

$$
\begin{aligned} t_e &= \frac{3 + 20 + 6}{6} = 4.83 \\ \sigma &= \frac{6 - 3}{6} = 0.50, \quad \text{Var} = 0.25 \end{aligned}
$$

| | $t_e$ | $\sigma$ | Variance |
|---|---|---|---|
| x | 6.00 | 0.67 | 0.44 |
| y | 4.83 | 0.50 | 0.25 |

**Answer:** $t_e$(x) = 6.00 and $t_e$(y) = 4.83. Activity **y** has the smaller SD (0.50) and variance (0.25), so y is more certain.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How do CPM and PERT differ in their time estimates?
   A. CPM uses three estimates and PERT uses one
   B. Both use three estimates
   C. CPM uses one deterministic estimate and PERT uses three
   D. Both use one estimate but different units
   Answer: C. CPM is deterministic with a single time; PERT is probabilistic with t_o, t_m and t_p. (Key point: Time estimates in CPM and PERT)

2. Which technique does time-cost trade-off (crashing) and which computes probability of completion using Z?
   A. PERT does crashing; CPM computes probability
   B. CPM does crashing; PERT computes probability
   C. Both do both
   D. Neither does either
   Answer: B. CPM performs time-cost trade-off, while PERT is mainly about time and computes the probability of completion using Z. (Key point: Time-cost trade-off)

3. Activity y has t_o = 3, t_m = 5 and t_p = 6. What is t_e?
   A. 4.83
   B. 5.00
   C. 4.67
   D. 5.17
   Answer: A. t_e = (3 + 20 + 6)/6 = 29/6 = 4.83. (Key point: Expected time of y)

4. x has SD 0.67 (variance 0.44) and y has SD 0.50 (variance 0.25). Which is more certain?
   A. x, because its SD is larger
   B. x, because its t_e is larger
   C. Neither, because the t_e values differ
   D. y, because its SD and variance are smaller
   Answer: D. A smaller SD and variance mean less spread in time, so y is more certain. (Key point: Which is more certain)

## Related in Project Engineering

- [Bar chart; expected time and variance](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Abar-chart-draw-adv-te-variance) — Project Engineering, chapter 3
- [Difference between CPM and PERT](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-vs-pert-difference) — Project Engineering, chapter 3, asked 2×
- [When to use bar chart, CPM, PERT](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Abar-chart-cpm-pert-situations) — Project Engineering, chapter 3
- [CPM and PERT and their uses](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-pert-uses) — Project Engineering, chapter 3
- [PERT mean and SD of two projects](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Apert-mean-sd-two-projects) — Project Engineering, chapter 3
- [Expected time of contractors (PERT)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Apert-contractor-expected-time) — Project Engineering, chapter 3

## Related in other subjects

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- [Bar chart vs CPM/PERT as planning tool](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Aplanning-tool-choice) — Construction Management, chapter 2, asked 3×
- [Short note: TE and TM modes](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Ate-tm-modes-rectangular-waveguide) — Electromagnetism, chapter 6, asked 2×
- [Difference between CPM and PERT](https://www.bctengineer.com/question.md?key=semester_7%2Fict_project_management%3Acpm-vs-pert) — ICT Project Management, chapter 8