A partially solved PERT problem is detailed in the table below. Times are given in weeks.

a$.$ Calculate the expected time and variance for each activity. Enter these values in the appropriate column in the table above. Include all start and finish times.

b$.$ Which path$($s$)$ form the critical path?

c$.$ What is the estimated time of the critical path?

d$.$ What are the project variance and the project standard deviation?

e$.$ What is the probability of completion of the project within $31$ weeks?