If 92.75 mg of Na2CO3 is dissolved in 0.5mL of water, what would be the normality of the solution after the addition of 0.67 mL of water.

0.09275g/molar mass = mols Na2CO3

(We assume, I suppose, that the volumes of water are additive--they aren't always additive) so add 0.67 mL + 0.50 mL and convert to L.
M = mols/L.
For N = M x 2.