A proposed bridge is supported at two ends and one a center pier. Although the design allows for relative settlements of the foundations, the engineer needs to keep these settlements within limits. Settlements caused by the sum of numerous dead loads and impacts of moving vehicles are assumed to be normally distributed, with the variability arising from the effects on the soil by the foundation. By correlating with test results from similar structures and soil conditions, estimates of the settlements were made as follows Bridge Mean Settlement (in) Std.Dev. (in) Left end 3 1 Center pier 5 1.5 Right end 3 1 If both left and right end foundations on the banks are stabilized so that their settlements are negligible, specify the maximum allowable relative settlement of the center pier for the design engineer so that any maximum relative design settlement would exceed this value with a probability of only 0.0001.