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

Answer:

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

Step-by-step 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:

$Z = \frac{X - \mu}{\sigma}$

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 $\mu = 22, \sigma = \sqrt{2.77}$

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

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

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20 - 22}{\sqrt{2.77}}$

$Z = -1.2$

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

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