How much work will the Normal do?

Although, it is very intuitive to think that the person gets the energy needed for the jump by the work done of the normal reaction. However, this is not true at all.

Work done is the product of force and the displacement of the point of application of the force.

If we keep our concentration at the point of contact (feet), we will find that during the push, his feet remains intact with the ground and their displacement is zero. Therefore, the work done by the normal reaction is zero.

The energy he gets for jumping is through his muscles which convert the muscular energy in the kinetic energy.

All of the "forces" are internal to the body and are in the form of tension in the muscles, which produces torques around the joints. These torques are converted into translational motion by counter rotating joints that convert it back into translational motion, which accelerates the center of mass upwards. The momentum gained is enough to lift your entire body off the ground. The normal force acting the foot from the ground doesn't move any thing so that does no work. However, it can take away energy if it is not rigid, say a soft springy child safe surface could actually reduce the upward motion.