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20 June, 01:39

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

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Answers (1)
  1. 20 June, 04:29
    0
    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.
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