Question

A project completion time can be assumed to be represented by a normal distribution curve The project is expected to complete in 36 weeks with a path variance of 6.67 Base on the information provided, calculate: a. Calculate the probability that the project will be completed in 39 weeks or less b. The probability that the project will be completed in between 33.5 and 38 weeks c. With 95 percent probability, calculate the date the project can be completed.

Answer 1

Mean = 36 weeks

variance = 6.67

standard deviation = sqrt(variance) = 2.58 weeks

1. Probability that project completed in 39 weeks or less.

= 1 - probability that project will be completed in 39 weeks or more
i.e Z= 1 - ((X-Mean)/Standard deviation)
Z = 1 - ((39-36)/2.58)
Z = 1 - 0.1230 ( the 0.8770 value is brought from Z table)
Z = 0.8770
i.e with 87.70% probability we can say that the project will be completed in 39 weeks

2) What is the probability that it will be completed in 33.5 weeks and 38 weeks

= 1 - (probability that it will be completed in 33.5 weeks) - (probability that it will take more than 38 weeks)
= 1 - ((33.5-36)/2.58) - ((38-36)/2.58)
= 1 - (-0.97) - (0.78)
= 1 - (0.166) - (0.2177) ( 0.166, 0.2177 values are brought from Z table
= 0.6163
= 61.63% probable that it will be completed in 33.5 weeks and 38 weeks od time.

3) Z = 95 percent probability
Where Z = 1.645

i.e 1.645 = ((X-36)/2.58)
X = (1.645*2.58) + 36
X = 4.24 + 36
X = 40.24 weeks
In 40.24 weeks it is 95% probable that the projeect will be completed