# Exercise to calculate the delivery date of a project for a probabilityProbability Calculator - PERT Method

### Problem Data

It is required to calculate **The time where the project will be completed on schedule with a probability of 0.9 ** according to the following data:

- Expected Project Time (T
_{E}) - 36.3333 days
- Project Variance (σ
^{2}) - 5.2221
- Description
**Exercise to calculate the delivery date of a project for a probability**You have a project with an expected completion time of 36.333 days and a variance of 5.2221. What delivery date gives the project a 90% probability of on-time completion?

## Solution

The following are the detailed calculations and graphs to obtain **The time** according to the data provided:

### Step 1:

The **PERT Method** is based on two assumptions:

- Project completion times follow a normal probability distribution.
- The times of the activities are statistically independent.

From these assumptions, the normal distribution curve (Gaussian bell) is used to represent the project completion dates. This distribution will indicate that the project has a 50% probability of finishing before the Expected Time (T_{E} = 36.3333 days) and a 50% probability of exceeding the Expected Time.

To calculate **The time where the project will be completed on schedule with a probability of 0.9** we will do the following:

Also:

Where:

**T:**Due date to be evaluated.**σ:**Standard Deviation of the Project. It is obtained from the square root of the Variance.

Replacing the values we would have:

For a probability of 0.9 the value of Z is 1.2816. Therefore:

**Note:** The normal distribution table is used to calculate the Z value..

Within **39.2619 days**, there is a 0.9 probability of completing the project on time.

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