A consulting company's senior manager has gathered the activity information for a proposal they are preparing for a client. Activity A B C D E F G Optimistic 2 2 4 1 3 1 2 Time estimate weeks Most Likely 4 6 5 2 5 3 4 Pessimistic 6 7 6 3 7 4 6 Immediate Predecessors A,B B C,D E,F a) Draw the network diagram. What is the expected completion time (state it explicitly)? What is the variance of project completion time? b) The deadline is 23 weeks. What is the probability of completing it on time? What is the probability of the project missing the deadline? c) What is the probability of finishing in 18.5 weeks or less? d) As project manager, you will be paid a bonus if you finish the project in 21 weeks or less. What is the probability of achieving the bonus? e) What is the probability of finishing between 21 and 23 weeks? f) What is the timeline that would achieve a 50% probability of finishing? What is the timeline that would achieve an 80% probability of finishing?