Proof about normal approximation to binormal

Question

Here q=1-p. I have got a hint about this question is np>=npq but I have no idea how this hint can be useful. Any help would be much appreciated.

Answer 1

Hint for (a): Multiply the inequality (which we assumed at the outset) $$\sqrt{npq}\ge 3$$ by $\sqrt{npq}$ on both sides, then apply the hint.

For (b), do the same as (a) but apply the analogous hint $nq\ge npq$.

For (c), there are four inequalities to prove. Argue them one at a time. You'll see two of them are re-expressions of (a) and (b); the remaining two should be obvious.