The new director of special events at a large university has decided to complete

Question

The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Use Table B and Table B1.

Assuming the project begins now, what is the probability that the project will be completed before: (Round your z-value to 2 decimal places and all intermediate probabilities to 4 decimal places. Round your final answers to 4 decimal places.)

Expected Duration (weeks) Variance 1.21 2.?? 1.00 2.89 1.44 Path 180 12 15 14

Explanation / Answer

a) For each path, calculate z-stat for x=16 by the following formula

z = (x-m)/s , where m is the expected duration of the path and s is the standard deviation. (standard deviation is square-root of variance)

Next, Look for probability corresponding to the z-stat in the standard normal tables

Probability of graduation time within 16 weeks = 1*1*1*0.7224*0.9525 = 0.6881

b) Similarly, calculate z-stat for x=15 and then look for probability corresponding to the z-stat in the standard normal tables

Probability of graduation time within 15 weeks = 1*1*0.9987*0.5000*0.7967 = 0.3978

c) Similarly, calculate z-stat for x=13 and then look for probability corresponding to the z-stat in the standard normal tables

Probability of graduation time within 13 weeks = 0.9968*0.9998*0.8413*0.1190*0.2033 = 0.0203

Path Expected Duration Variance Std Dev. Z-stat Probability A 10 1.21 1.10 5.45 1.0000 B 8 2.00 1.41 5.66 1.0000 C 12 1.00 1.00 4.00 1.0000 D 15 2.89 1.70 0.59 0.7224 E 14 1.44 1.20 1.67 0.9525

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