133k views
4 votes
A project whose critical path has an estimated time of 120 days with a variance of 100 has a​ 20% chance that the project will be completed before which day​ (rounded to nearest​ day)?

A.120
B.220
C 98
D.112
E.124

1 Answer

4 votes

Final answer:

Using the Z-score for a 20% likelihood in a normal distribution and the given mean and variance, the project has a 20% chance of completion before day 112. The calculation involves converting the Z-score to the corresponding time.

Step-by-step explanation:

To determine the day by which there is a 20% chance that the project will be completed, we can use the concept of the normal distribution and Z-scores because the distribution of project completion times is often modeled as normal.

The Z-score for the given percentage can be found using the standard normal distribution table or a Z-score calculator. A 20% chance corresponds to a Z-score of approximately -0.84 (looking up the value where the left tail of the distribution includes 20% of the area under the curve).

Once the Z-score is identified, we use the following formula to find the time associated with this Z-score:

Z = (X - μ) / σ

Where:
• Z is the Z-score (-0.84),
• X is the unknown time (the day we want to find),
• μ is the mean (the estimated time of 120 days),
• and σ is the standard deviation (the square root of the variance, which is √100, or 10 days).

Plugging the values in, we get:

-0.84 = (X - 120) / 10

X = 120 + (-0.84 * 10)

X = 120 - 8.4

X = 111.6

Since we need to round to the nearest day, the project has a 20% chance of being completed before day 112, which corresponds to the options provided.

User Anjan Talatam
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.