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CMA Final · Strategic Cost Management · Network Analysis - PERT, CPM

The critical path of a project has three activities with (optimistic, pessimistic) times of (2, 14), (5, 11) and (1, 13) days. Its expected length is 40 days. Assuming a normal distribution of project duration, what is the probability of completing within 46 days? (Use Φ(1)=0.8413, Φ(2)=0.9772, Φ(0.67)=0.7486.)

The probability is 97.72%. The critical path variance is 4+1+4 = 9, so the standard deviation is 3 days. Z = (46−40)/3 = 2, and the normal table gives 0.9772. Dividing by the variance instead of the standard deviation would be an error.

  1. A74.86%
  2. B84.13%
  3. C97.72%Correct
  4. D50.00%

Explanation

Activity variances are ((b-a)/6)^2 = 4, 1 and 4, so the path variance is 9 and the standard deviation is 3. Z = (46-40)/3 = 2, giving a probability of 0.9772. Using 9 instead of 3 as the standard deviation gives Z = 0.67 and 74.86%, which is wrong.

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