  Let G be a finite group and N be a non-trivial normal subgroup of G, such
that the average character degree of irreducible characters in Irr(G|N) is less
than or equal to 16=5. Then we prove that N is solvable. Also, we prove the
solvability of G, by assuming that the average character degree of irreducible
characters in Irr(G|N) is strictly less than 16=5. We show that the bounds are
sharp.
