A steel (E = 30 × 106 psi) cantilever beam of length 10 ft is required to support a concentrated load at its free end whose mean value is 500 lb and whose standard deviation is 100 lb. If the cross section of the beam is rectangular with a 2" width, how deep should the beam be so that there is a 99.9% probability that its deflection at the free end is less than 3"?
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