$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessors$]],\backslash$table$[[$Most$],[$Optimistic$],[$Time$]],\backslash$table$[[$Most$],[$Likely$],[$Time$]],\backslash$table$[[$Most$],[$Pessimistic$],[$Time$]],\backslash$table$[[$Expected$],[$Time$],[($ET$)]],$Variance$],[$A$,-,2,3,6,,],[$B$,$A$,3,4,5,,],[$C$,$B$,1,2,4,,],[$D$,$B$,3,5,6,,],[$E$,$C$,3,4,5,,],[$F$,$D$,3,3,4,,],[$G$,$E$,$F$,1,2,3,,]]$

Step $1.$ Calculate the expected time for each activity.

Step $2.$ Identify the different paths in the network and total activity time on path.

$($Use the expected times of each activity for this calculation$).$

Path $1$:

Time: $q,$

Path $2$:

Time: $q,$

Step $3.$ Identify the critical path$($s$)$ on the network. The critical path is the one having the longest total activity times AND also has no slack.

Critical Path:

Total Time: $$

Estimating the Probability of a Completion Jate

Step $1.$ Calculate the variance of completion times from the most optimistic and most pessimistic completion times and insert in table.

Step $2.$ Find the total variance for each path in the network. The total variance along a path is simply the sum of the individual variances of activities on the path.

Path $1$:

Total Variance:

Path $2$: $q,$ Total Variance:

Step $3.$ Find the probability of a scheduled completion date of less than $17$ days.

a$.$ Sketch out the project mean and project standard deviation assuming a normal distribution with mean and standard deviation found above. Remember the standard deviation is the square root of the variance!

$q,$

b$.$ Now, find the $z$ value for a scheduled completion date of day $17$ on the critical path using the formula:

$z=(\frac{D_T-E{T}_p}{\sqrt[\phantom{2}]{{}_p^2}})=$

$q,$

Using the $z$ value, a probability value can be found.