McGee Carpet and Trim installs carpets in commercial offices.  Andrea McGee has been very concerned with the amount of time it took to complete several recent jobs.  Some of her workers are very unreliable.  A list of activities and their optimistic completion time, the most likely completion time, and the pessimistic completion time (all in days) for a new contract are provided in a given table.  Following are the activities that are required to install the carpets in the offices: Activity 1 (Measure office room dimensions), Activity 2(Estimate cost), Activity 3 (Material Requisition), Activity 4 (Workforce Requisition), Activity 5 (Special Tool Requisition), Activity 6(Installation), Activity 7 (Inspection and customer acceptance).

Activity 2 starts immediately after Activity 1. Activity 3, Activity 4, and Activity 5 start concurrently after Activity 2. Activity 6 does not start until after Activity 3, Activity 4, and Activity 5 are completed. The carpet installation project is complete after Activity 7 is completed. If OT = Optimistic Time, MT = Most Likely Time, and PT = Pessimistic Time, use Program Evaluation Review Estimate (PERT) to compute the statistical time for each activity in the table shown below.  

Activities	OT	MT	PT
Activity 1	4	6	14
Activity 2	5	12	16
Activity 3	7	15	23
Activity 4	13	16	28
Activity 5	17	20	35
Activity 6	20	32	50
Activity 7	5	6	13

Also, (a) Determine the expected completion time and the variance for each activity (b) Determine the total project completion time and the critical path for the project.  (c) Determine Early Start (ES), Early Finish (EF), Late Start (LS), and slack for each activity.  What is the probability that McGee Carpet and Trim will finish the project in 40 days or less?