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**1.**There are four activities along the critical path for a project. The expected values and variances of the completion times of the activities are listed here. Determine the expected value and variance of the completion time of the project.

**2.**The operations manager of a large plant wishes to overhaul a machine. After conducting a PERT/CPM analysis he has developed the following critical path.

1.Disassemble machine

2.Determine parts that need replacing

3.Find needed parts in inventory

4.Reassemble machine

5.Test machine

He has estimated the mean (in minutes) and variances of the completion times as** **follows.

Determine the mean and variance of the completion time of the project.

**3.**Refer to Exercise 7.57. Find the probability that the project will take more than 60 days to complete.

**4.**The mean and variance of the time to complete the project in Exercise 7.58 was 145 minutes and 31 minutes. What is the probability that it will take less than 2.5 hours to overhaul the machine?

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