How to calculate probability of completing a project on time

Asked by admin @ 22/11/2021 in Mathematics viewed by 277 People

A project has a mean completion time of 54 weeks and a standard deviation of the project completion time of 2.95 weeks. What is the probability of completing the project within 52 weeks? Please put your answer in terms of a probability (i.e. a number between 0 and 1), and not a percentage.

Answered by admin @ 22/11/2021

Answer:

0.2483

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 54, \sigma = 2.95$

What is the probability of completing the project within 52 weeks?

This is the pvalue of Z when X = 52.

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

$Z = \frac{52 - 54}{2.95}$

$Z = -0.68$

$Z = -0.68$ has a pvalue of 0.2483

So the answer is 0.2483

How to calculate probability of completing a project on time

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