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Published on Monday, April 20, 2009 - 02:21 PM
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As the project manager for a newly charted project you have developed the following information based on the input from your project team members: Optimistic time for project completion = 25 weeks, pessimistic time for project completion is 50 weeks, most likely time for project completion is 40 weeks. Using the weighted average technique you have determined that there is a 95% probability that the project will be completed:
a. Between 35 and 43.34 weeks
b. Between 30.83 and 47.51 weeks – correct answer
c. Between 26.66 and 51.61 weeks
d. Between 30.83 and 51.61 weeks
To solve this problem you must first determine the weighted average. Then calculate the standard deviation.
Te = 39.17 This is the mean based on the formula :
Te = {optimistic + 4 (most likely) + pessimistic} / 6
Standard Deviation = 4.17
{Pessimistic – optimistic} / 6
One standard deviation from the mean = 39.17 + 4.17 = 43.34
Two standard deviations from the mean = 39.17 + 4.17 +4.17 = 47.51
One standard deviation from the mean = 39.17 – 4.17 = 35
Two standard deviations from the mean = 39.17 – 4.17 – 4.17 = 30.83
3 standard deviations = 26.66 or 51.68
Considering normal distribution the probability is:
68% chance the project will complete within 1 standard deviation from the mean = 35 to 43.34
95% chance the project will complete within 2 standard deviations from the mean = 30.83 to 47.51
99.74% chance the project will be completed within 3 standard deviations from the mean.
It is important to remember this information: In statistics 68-95-99.7 rule, or three-sigma rule, or empirical rule, states that for a normal distribution, almost all values lie within 3 standard deviations of the mean.
About 68% of the values lie within 1 standard deviation of the mean (or between the mean minus 1 times the standard deviation, and the mean plus 1 times the standard deviation). In statistical notation, this is represented as: μ ± σ.
About 95% of the values lie within 2 standard deviations of the mean (or between the mean minus 2 times the standard deviation, and the mean plus 2 times the standard deviation). The statistical notation for this is: μ ± 2σ.
Almost all (99.7%) of the values lie within 3 standard deviations of the mean (or between the mean minus 3 times the standard deviation and the mean plus 3 times the standard deviation). Statisticians use the following notation to represent this: μ ± 3σ.
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