Problem 1 (25 pts) Consider a demand or load versus capacity or strength relation, , where R denotes the capacity and S the demand. Assume that capacity is described by a normal distribution with Mr = 200, Or = 40, and the demand is also described by a normal distribution with us = 100, Os= 30. Estimate the probability of failure by performing 5 Monte Carlo simulations by hand, using the following 10 random numbers that are produced from a normal distribution N[0,1] (normal distribution with mean zero and standard deviation one), i.e., -0.048, 0.583, -1.518, -0.136,-1.866, 1.269, 2.341, 0.451, 1.437, 0.999, and do not use any of the numbers more than once. Note: due to the limited number of simulations you may obtain that is zero, so it is important to show all 5 simulations. You can use Excel to perform the simulations, but the above 10 numbers should be used. In that case, the Excel file should be uploaded in D2L as part of the exam