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Table Summary: A table with $5$ columns. Column $1$ lists the job number. Column $2$ lists the corresponding predecessor jobs. Columns $3$ to $5$ are titled $a,m,$ and $b.$ They are merged and titled time in days.

$\backslash$table$[[$Job No$.,$Predecessor Job$($s$),],[$a$,m,b,,],[1,-,2,3,4],[2,1,1,2,3],[3,1,4,5,12],[4,1,3,4,11],[5,2,1,3,5],[6,3,1,2,3],[7,4,1,8,9],[8,5,6,2,4,6],[9,8,2,4,12],[10,7,3,4,5],[11,9,10,5,7,8]]$

Construct the appropriate network diagram.

Indicate the critical path.

What is the expected completion time for the project?

You can accomplish any one of the following at an additional cost of $$1,500$ :

$(1)$ Reduce job $5$ by two days.

$(2)$ Reduce job $3$ by two days.

$(3)$ Reduce job $7$ by two days.

If you will save $$1,000$ for each day that the earliest completion time is reduced, which action, if any, would you choose?

What is the probability that the project will take more than $30$ days to complete?