Construction of a new ofce block is being planned. The start date has been agreed upon and fixed but there is uncertainty about how many weeks the various activities will take. The planning team accept that, for each activity, a reasonable model of the variation in duration would be the beta distribution. They have therefore prepared for each activity estimates of the optimistic, most likely and pessimistic durations. These estimates are given in the table below along with the immediately preceding activities. Immediately . . . . . . . . . . OptImIstIc Most lIkely PeSSImIStIC Activity DescnptIon precedIng . . . activity(ies) duratIon duratIon duratIon Arrange contracts - 4 7 16 Clear and 2 9 l Install drains D,E 18 39 J Build parking spaces F 19 30 K Final wiring G,H 2 4 12 L P'umbi"9 I 10 15 26 a) Assuming a beta distribution of activity durations, calculate the mean duration and standard deviation of all activities using the three estimates of activity duration given in the table. [4 points] b) Construct a network diagram for this problem using the mean durations, calculate the total oat for all the activities (Show LS (Fo||.), ES(Prec.) for all activities) and hence identify the critical path. What is the mean completion time for the project? What is the standard deviation of the critical path? [30 points] c) What is the 92% 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 that the project can be completed within 79 weeks. [4 points] e) What is the probability that the project will be completed between 78 and 82 weeks? [4 points] f) Answer the project manager's question: \"I want to tell the client that there is a 19.77% chance that the project will take longer than X weeks to be completed what gure should I give them (i.e. nd X)?\" [4 points] Upload a file showing your diagram and activity schedule (LS, ES. Total oat) and answer the questions above. You can either do it electronically or using a pen and paper and then uploading a picture of your work