Eggs or Flour

Here's a puzzle I remember from a high school science lecture (somewhat modified). This assignment was given preceding an experiment:

Still working at the Princeton Institute for Advanced Studies, and still the cook, you awake one morning to find the power out. Again. Of course, this isn't a problem since you have devised numerous methods of timing all your dishes to cesium precision using only two hour glasses. Unfortunately, two shipments of ingredients have just come in. One shipment is twelve boxes containing eggs, the other is twelve boxes containing flour. You need the flour right away, but without proper refrigeration the eggs will go bad. The eggs will be fine in their boxes, but if you open a box of eggs looking for the flour, those eggs will be wasted.

The boxes are indistinguishable by appearance- your supplier uses the same boxes for both. Also, the supplier's packing standards are not particularly high. Not only may the eggs break if your examination of the boxes involves high-speed collisions, but each box of the shipments do not have a constant quantity inside.

This is what you know:

• The flour is all-purpose bleached flour
• The eggs are Grade A Extra Large brown
• The lightest box weighs 47.85 ounces
• The heaviest box weighs 65.63 ounces
• An empty box weighs 5.02 ounces
• The kitchen scale is accurate to 1/100th of an ounce.

How can you safely choose a box containing flour without the risk of accidentally opening a box of eggs?

EXTRA CREDIT

Above I mentioned this puzzle was given preceding a science experiment. What was the experiment?

Show your work.