Question

Joe used a project management software package and has determined the following results for a given project.: Expected completion time of the project = 22 days Variance of project completion time = 2.77 What is the probability of completing the project over 20 days?

Answer 1

0.1151 = 11.51% probability of completing the project over 20 days.

Explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Expected completion time of the project = 22 days.

Variance of project completion time = 2.77

This means that
`\mu = 22, \sigma = √(2.77)`

What is the probability of completing the project over 20 days?

This is the p-value of Z when X = 20, so:

`Z = (X - \mu)/(\sigma)`

`Z = (20 - 22)/(√(2.77))`

`Z = -1.2`

`Z = -1.2` has a p-value of 0.1151.

0.1151 = 11.51% probability of completing the project over 20 days.