An online trading company is facing stiff competition and has decided to install a new computer system to allow faster and more efcient processing of customer orders, customer enquiries and the company's dealings with suppliers. The activities that will be necessary to install the new system and have it routinely operating as intended are listed in the table below. Activity ID Follows Estimates of durations (weeks) Shortest Most likely Longest Install equipment A -- b 12 Develop system B -- 3 7 11 Recruit new staff C -- 2 5 8 Test equipment D A 2 16 10 Test logic of system E B 1 j4 7 Induction of new staff F C 2 M 6 Introduce to senior staff G C 1 2 3 Training on new system H A, E, F 5 7 9 Check for errors | A, E, F 2 5 8 Final debugging J D 2 3 4 Trial runs K G. l 3 8 13 REQUIRED a) Calculate mean duration and standard deviation for all activities using the beta distribution. (4 points) b) Construct a network diagram for this problem using the mean durations calculated in part (a), calculate the total float for all the activities. and hence identify the critical path. What is the mean completion tim for the project? What is the standard deviation of the critical path? (30 points) 0) What is the 85% condence interval for the length of the critical path? (4 points) d) Assuming that the probability distribution of the length of the critical path can be approximated by a normal distribution with the mean and standard deviation calculated in part (b), calculate the probability th: the new computer system will be ready for routine operation within 27 weeks. (4 points) e) What is the probability of completing the project between 19 and 26 weeks? (4 points) f) Answer the project manager's question: \"I want to tell the client a project length which I am 79.95% sure that we can meet - what gure should I give them?" (4 points)