$1.$ Develop a network diagram $($AKA precedence diagram$).$

$2.$ Calculate the expected duration for each activity. Determine the ES$,$ EF$,$ LS LF$,$ and slack for each activity.

$3.$ Using your calculations determine the critical path and highlight it on your diagram.

$4.$ Calculate the variance and standard deviation of the project's total duration. What is the probability that the project will be finished within $270$ days $($that is $270$ days or less$)?$