3→4 14 16 18 32 32 74 5→6 12 (a)On the basis of the estimates just listed, calculate the expected value and standard deviation of the time required for each activity (b) Using expected times, determine the critical path for the project Solution:(a) the expected value and standard deviation are listed in the following table Activit OptimisticMost Pessimisti Expected Variance Standard y estimate likely c estimate value deviation estimate 36 3.33 0.444 0.67 32 32 3→6 74 53.67 32.11 5.67 4→5 24 1667 5→6 6 20.33 7.11 2.67 17.67 (b) 8 1000 The critical path for the project is 1-3-6-7, the expected finish time for the whole project is 100 weeks5 3→4 3→5 3→6 4→5 5→6 5→7 6→7 14 32 40 12 16 26 12 16 32 52 16 20 34 16 18 32 74 24 26 42 30 (a) On the basis of the estimates just listed, calculate the expected value and standard deviation of the time required for each activity. (b) Using expected times, determine the critical path for the project. Solution: (a) the expected value and standard deviation are listed in the following table Activit y Optimistic estimate Most likely estimate Pessimisti c estimate Expected value Variance Standard deviation 1→2 1→3 2→6 3→4 3→5 3→6 4→5 5→6 5→7 6→7 28 22 26 14 32 40 12 16 26 12 32 28 36 16 32 52 16 20 34 16 36 32 46 18 32 74 24 26 42 30 32 27.67 36 16 32 53.67 16.67 20.33 34 17.67 1.77 2.77 11.11 0.444 0 32.11 4 2.77 7.11 9 1.33 1.67 3.33 0.67 0 5.67 2 1.67 2.67 3 (b) The critical path for the project is 1→3→6→7, the expected finish time for the whole project is 100 weeks. 1 2 3 4 5 6 7 32 28 36 16 32 54 17 20 34 18 32 46 14 82 82 0 100 100 0 61 62 1 44 45 28 1 28 0 0 0 0