Problem 1 (20 marks) Please note that this problem has six parts You may need to scroll the screen down, navigate left and night to see the whole problem Clearly label your parts when answering You are allowed three pictures for this problem Must use pen to answer Show all calculations result to FOUR PLACES AFTER THE DECIMAL POINT (except when all succeeding digits are zeros) Must Show all calculations/steps Failure to do so will result in a score of Teven final answer is correct Pond Furnace Installation Services (PFIS) is owned by Jonna She is very concerned with the amount of time it took to complete several recent jobs. Some of her workers are very unreliable with respect to time. A list of activities and their optimistic completion time (a), the most likely completion time (m) and the pessimistic completion time (b) for a new contract are determined. Based on the assumption that the activity times follow a beta distribution, the expected activity time and the standard deviation of each activity are calculated for you and are given in the table below: Activity Standard Deviation B D E F G H immediate Expected Predecessor (s) Time (days) None 13 None 4 None 2 7 BD AE AE 3 F 6 G 11 CE 17 H1 8 1.6667 0.6667 0.3333 0.3333 0.6667 4 9 1 3333 J K 0.3333 1.6667 2 a) b) c) Construct a network diagram and determine ES EF, LS, LF and slack for each activity Determine the expected project completion time and the critical pathis What is the probability that PFIS will finish the project within 40 days? What is the probability that PFIS will take more than 35 days to complete the project? What is the probability that PFIS will take more than 35 days but less than 41 days to complete the project? If Jonna wants to complete the project with a 96% assurance, then how many days from the due date should she need to start the project? You can leave your answer in decimals. 1)