A student of mass \(50\text{ kg}\) stands on a force platform inside an elevator cab that moves along a vertical track. The platform measures the vertical normal force exerted on the student. The acceleration \(a\) of the elevator as a function of time \(t\) is shown in the graph, where the upward direction is defined as positive. What is the average normal force exerted on the student by the force platform over the time interval from \(t = 0\text{ s}\) to \(t = 5.0\text{ s}\)?