# Project Probability with Variance Given

A project has an expected duration of 34 weeks with a critical path variance of 6. Suppose the project network is given and the critical path is identified on the network. Suppose the normal time, crash time, and the associated cost for each activity is given. You have been asked by your supervisor to prepare a research paper that addresses the follow criteria:

- What is the probability that the project will be completed in 32 weeks or less?

- If the project is to be shortened by four days, list the process you would take to determine which activities, in order of reduction, would be shortened and the resulting cost.

- Describe project cost and the requirements for it's determination and application in a production facility.

- Analyze implications of changes in the parameters of project timing and cost determination.

- Evaluate application of project cost and timing concepts on a firm's business operations.

#### Solution Preview

Project Probability

If the expected duration of project is 34 weeks, then the probability of project will be calculated through following formula:

Z = (Winston & Albright, 2011)

Where, t = 32 weeks

v = variance (6)

Then, Z=

= -0.33

On the basis of cumulative normal probability tables, p [Z ≤ 0.33] =0.3707 (Standard Normal Cumulative Probability Table.

So, to complete the project in 32 weeks is 37%.

The project manager plays an important role in shortening the project schedule. If the project is to be shortened by four days, the project manager should study fast-tracking or shift to advances technology to complete the project. For reducing duration, project manager should list the requirement of labor, equipment and materials for completed tasks. Generally, there are two ways to reduce a project schedule that is task spitting and crashing (Nicholas & Steyn, 2012). In the task splitting, project manager will split down large task into two or more smaller tasks. On the other hand, through crashing method, project manager will add extra resources to a task to increase its ...

#### Solution Summary

The expert examines project probability with variances given.