Task 3: (8 marks) A property management firm is responsible for maintenance, rental and day-to-day operation of a large apartment complex. The manager of this firm is concerned about the potential cost for replacing air conditioner (A.C.) compressors used in this complex, and thus would like to simulate number of compressor failures occurring in each of the next 20 years. Based on the data from a similar complex managed by this firm, he managed to establish a table of relative frequency of .. compressor failures during a year as shown in the table below A.C.Relative frequency Number of Compressor failures (Probability) 0.06 0.13 0.25 0.28 0.20 0.07 0.01 0 4 Conduct one simulation for each of the 20 years BY HAND (NOT using Excel) for the manager, to simulate the number of .. compressor failures for each of the 20 years, using the 20 random numbers given in the table below (ie, one random number for each of the 20 simulations, Simulation 1 to 20). These numbers were generated randomly from the uniform distribution (0, 1) 2 6 10 0.362 0.445 0.162 0.045 0.001 0.683 0.3990.232 0.4970.794 12 13 14 15 16 17 18 19 20 0.968 0.73 0.663 0.495 0.75 0.291 0.561 0.135 0.586 0.235 a) Show how you have carried out the 20 simulations and related, and also write down resulting number of A.C. compressor failures for each of the 20 years (simulations) Based on the results from those 20 simulations, answer the following questions i. s it common to have no more than two compressor failures per year? Justify your answer. ii Out of the 20 simulations (ie, years), how many compressor failures will there be per year (ie, on b) average)? How many will you expect if according to the probability table given in the task