Write a corresponding predicate logic sentences for the following "Some sleepy students do not answer any question."?

Question

My answer is that

Let $A$ represent a student that answers any question, and let $S$ represent a sleepy student. Then, $\exists x (S(x)\wedge \neg A(x))$.

Is it correct?

Answer 1

Exists x with (x is sleepy student and
not for all q, (q is question implies x answers q)),

which is equivalent to

Exists x with (x is sleepy student and
exist q with (q is question and not-(x answers q)).

However “Some sleepy students do not answer any question.”
is liguishically awkward.
"Some sleepy students do not answer any questions.”
does not have that semantic difficulty but has a different meaning. Namely:

Exists x with (x is sleepy student and
for all q, (q is question implies not-(x answers q))).