3 Consider a simple bolted connection between structural members. in addressing the ques- tions in this problem, assume that the total load capacity of the bolted connection is the sum of the capacities of the individual bolts. Ebr the critical failure mode, the load capacity of individual bolts can be modeled as a Normal random variable with mean u. = 100 [RN] and standard deviation 0' = 2 [UN]. The load capacities of the bolts are statistically independent5. Figure 3: An example of a sequence of complex bolted connections in a bridge structure. [http : l/miliclu'ivor. com/phottie/461354860H08/5025054381I] a What is the average and standard deviation of the load capacity for one-bolt connec- tions? (Yes, this is the obvious answer.) 33. What is the average and standard deviation of the load capacity for two-bolt connec- tions? 0. Estimate and plot and/or tabulate the averages and standard deviations of the load capacity of nbolt connections, for 11. = l, 2, . . . , 10. d. Plot and/or tabulate the number of bolts in a connection \"n.\" (on the abscissa: hor- izontal axis), versus the probability that the load capacity of a connection is greater than or equal to no (on the ordinate: vertical axis). The plot and/or table should include the range 11 = 11 2, . .. 10. Hint: this is not a direct extension of the previous parts. This question can be answered using a relatively simple analytic formula