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

The critical path of a PERT network has an expected duration of 50 days and a variance of 16 days². Assuming the normal distribution applies, and that the area under the standard normal curve up to Z = 1 is 0.8413, what is the probability that the project will be completed within 54 days?

The probability is 0.8413. The standard deviation of the critical path is 4 days, so Z = (54 − 50)/4 = 1, and the cumulative normal area at Z = 1 is 0.8413. The figure 0.1587 would be the chance of exceeding 54 days.

  1. A0.8413Correct
  2. B0.1587
  3. C0.6915
  4. D0.9772

Explanation

The standard deviation is √16 = 4 days. Z = (54 − 50)/4 = 1, so the probability is 0.8413. The 0.1587 option is the probability of exceeding 54 days (1 − 0.8413). The 0.6915 option comes from wrongly dividing by the variance, which gives Z = 0.25 rather than using the standard deviation.

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