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The following table represents the set of activities required to complete a project, along with their time estimates for PERT calculations.

a. Using the data in the table, calculate the expected time (ET) and variance for each activity.

Job number--Predecessor Job(s)--a--m--b--expected time (ET)--variance

A----3--5--7

B--A--3--4--5

C--A--2--3--4

D--B,C--3--4--11

E--C--1--3--5

F--D,E--6--8--10

b. [Sketch the network diagram for the project on a sheet of paper. YOU DO NOT HAVE TO SUBMIT THE SKETCH AS PART OF YOUR ANSWER].

c. List each unique path through the network. For example, "A, B, C" would indicate a path consisting of activity A, followed by activity B, which is followed by activity C.

d. Indicate the critical path. (You can by inspecting the paths -- you do not have to calculate ES, EF, LS, LF.) What is the expected completion time for the project?

e. What is the probability that the project will be completed in 21 days or less?

f. What is the probability that the project will take more than 21 days to complete?