The parking superintendent is responsible for snow removal at his parking garage. the probabilities for the number of days per year requiring snow removal are shown in the chart below. these probabilities are independent from year to year. the superintendent can contract for snow removal at a cost of $500 per day. alternatively, he can purchase a snow-removal machine for $40,000. it is expected to have a useful life of 10 years and no salvage value at that time. annual costs for operating and maintaining the machine are estimated to be $14,000. marr (minimum attractive rate of return) is 10% per year. number of days per year probability 20 0.15 40 0.15 60 0.35 80 0.30 100 0.05for the following questions, determine an analytical solution: a)determine the mean and standard deviation of the present worth of the savings resulting from purchasing the snow-removal machine.($)b)assuming the present worth is normally distributed, what is the probability of a positive present worth of the savings resulting from purchasing the machine? (%)c)for the following questions, determine a simulation solution using @risk: d)using a latin hypercube simulation with 10,000 iterations, estimate the mean and standard deviation of present worth and the probability of positive present worth. e)using a monte carlo simulation with 10,000 iterations, estimate the mean and standard deviation of present worth and the probability of positive present worth.