The parallel activity paths and their estimated durations as follows : 1-2-4 = 4

Question

The parallel activity paths and their estimated durations as follows :

1-2-4 = 4 + 6 = 10 weeks

1-3 -4 = 3 + 9 = 12 weeks

By virtue of having the longer duration, 1-3-4 is the critical path and estimated project duration is 12 weeks

Variance of the critical path

= ( Std deviation 1-3)^2 + ( std deviation 3-4)^2

= 0.62^2 + 1.90^2

= 0.3844 + 3.61

= 3.9944

Standard deviation of critical path

= Square root ( 3.9944)

= 1.998

Let Z value corresponding to the probability of finishing the project in 11 weeks = Z1

Therefore,

Expected completion time + Z1 x Standard deviation of critical path = 11

Or, 12 + 1.998.Z1 = 11

Or, Z1 = - 0.50

Corresponding probability for Z1 = - 0.5 as derived from standard Normal distribution table

Is 0.30854

YES, BECAUSE THE PROBABILITY OF FINISHING ON SCHEDULE IS ONLY ABOUT 0.30854

Answer to question b :

Incurring a penalty of at least $5000 means delaying the project by at least 1 week from scheduled completion time of 11 weeks. That means project duration will be 12 weeks or more. Since 12 weeks is the expected ( mean project duration) , probability of finishing the project in 12 weeks or more as per standard normal distribution table = 0.5

PROBABILITY OF INCURRING A PENALTY OF AT LEAST $5000 IS 0.5

YES, BECAUSE THE PROBABILITY OF FINISHING ON SCHEDULE IS ONLY ABOUT 0.30854

Explanation / Answer

The project described in the following table has just begun. It is scheduled to be completed in 11 weeks.
Use Table B1 and Table B2.

a. If you were the manager of this project, would you be concerned? (Round your intermediate calculations to 2 decimal places and "Probability" values to 4 decimal places.)
  
(Click to select)  Yes  No  because the probability of finishing on schedule is only about  .

b. If there is a penalty of $5,000 a week for each week the project is late, what is the probability of incurring a penalty of at least $5,000? (Round your intermediate calculations to 2 decimal places and "Probability" values to 4 decimal places.)
  
Probability           

Reference links

Activity Estimated Time
(weeks) Standard Deviation
(wks.) 1-2 4 0.70 2-4 6 0.90 1-3 3 0.62 3-4 9 1.90

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