please answer the question and give an explanation:

3. A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times (probabilistic three-time estimates) for activities and precedence relationships. a) Construct a network diagram. (1 point) b) Calculate the expected time and variances for all the activities. (2 points) c) Identify all the paths (including path durations and path variances) and find the critical path (1 point) d) If the project takes more than 30 days for completion, the project manager will have to bear a penalty of $1,000; Find the probability of the project manager paying such a penalty. (2 points)