a. In this scenario, the independent variable is the size of the DNA fragments in the DNA ladder. This is what you are changing or manipulating when creating the standard curve.
b. The dependent variable is the distance that the DNA fragment migrated through the gel. This is what you are measuring in response to the sizes of the DNA fragments.
c. If you know the distance that a fragment of DNA migrated through a gel, you could use this information to solve for the dependent variable. You would use the distance migrated to determine the size of the unknown DNA fragment based on the standard curve created from the known sizes of the DNA ladder.