The probability that this project will be completed within 130 days is 0.8413.
Expected duration (ED) = (Optimistic + 4 x Most Likely + Pessimistic) ÷ 6.
Affirmative Action
41 Optimistic
Probability = 50
Negative = 59ED = (41 + 4 50 + 59) 6 = 50
50-minute duration
B. Activity
Positive = 54
60 is the most likely number.
Negative = 66ED = (54 + 4 60 + 66) 6 = 60
60-minute duration
C. Activity
Positive = 58
70 is the most likely number.
Negative = 82ED = (58 + 4 70 + 82) 6 = 70
70-minute duration
D's Activity
32 Optimistic
41 is the most likely number.
Negative = 44ED = (32 + 4 41 + 44) 6 = 41
41 minutes.
Project total duration = 50 + 60 + 70 + 41 = 221
Project completion time estimate = 221 days
The critical path's standard deviation is calculated using the following formula:
σ = P - O/6
Where indicates the critical path's standard deviation, P represents the pessimistic time, and O represents the optimistic time.
σ = 66 - 54/6 = 2.
Then there's the chance that this project will be finished in 130 days:
P(z -45.5) = 0 (due to negative value) z = (130 - 221) / 2 = -45.5
P(z -4.5) = 0 (as calculated from the normal distribution table)
As a result, the likelihood that this project will be completed within 130 days is 0.8413.
Complete question:
Consider the following work breakdown structure: Activity A B С D Start Node 1 1 2 3 Finish Node 2 3 Optimistic 41 54 58 32 Duration (days) Most Likely 50 60 70 41 Pessimistic 59 66 82 44 4 4 What is the probability that this project will be completed within 130 days? Multiple Choice O .9544 .8413 O 9987 .9772 190