Question

What is the probability that the following project will take more than 10 weeks to complete if the activity means and standard deviations are as shown below? (Round standard deviation to 2 decimal places and final answer to 4 decimal places.)

Use Table B.

Activity	Mean	Standard Deviation
1-2	5	1.3
2-3	4	1.0
1-3	8	1.6

Answer 1

Path 1 = (1-2) + (2-3) = 5+4 = 9

Path 2 = (1-3) - 8

So the critical path is 1

The standard deviation of the critical path = Square root of the variance of the critical path

Square root of (2.56+1.69) = Square root of (4.25) = 2.06

The probability of completing the work in 10 weeks = normal distribution of Z score

Z= (TS-TE) / DS of the critical path

Z = (10-9)/2.06 = 0.48

Normal of Z (0.48) = 0.6844

The probability of completeing the work within 10 weeks would be 68%