The following tasks lie on the critical path of a project:
Task Mean Completion Time St. Dev
A 4 0.6
B 5 0.2
E 2 0.1
F 6 1
H 2 0.2
M 6 0.1
The above task gives the mean completion time of each task (in days) and the standard deviation.
1. Based on this information, what is the probability that the project will be completed in 23 days or less?
a. Less than 5% but more than 3%
b. Less than 3%
c. More than 5% but less than 10%
d. None of the above

The correct answer is option (a)  Less than 5% but more than 3%

Explanation:

Scheduled time of project = 25

Calculating the activity variance, we have

Task     Mean time    Standard deviation        Variance

A                  4                               0.6               0.6² = 0.36

B                  5                               0.2               0.2² = 0.04

E                 2                                0.1                 0.1² = 0.01

F                 6                                  1                     1² = 1

H                 2                               0.2                 0.2² = 0.04

M                 6                               0.1                 0.1² = 0.01

Sum of variance = 0.36 +0.04 + 0.01 +1+ 0.04 + 0.01

                                =1.46

Standard deviation  = √variance

                                 =√1.46

                                 =1.2083

probability that the project will be completed in 23 days or less

z = 23-25 /1.2083

     = -1.65

which corresponds to prob. of 0.0494 = 4.94%

a is correct.