NP hard? Maximize the average for a subset of numbers

Given a set of real numbers, choose a subset to maximize the average subject to the average not exceeding a given threshold. Is it NP hard?

I think so, but I cannot come out with a proof. Thanks a lot!!

• Hint: for nonempty $S$, $\textrm{average}(S) \leq 0 \leftrightarrow \textrm{sum}(S)\leq 0$. – Yonatan N Jul 19 '18 at 4:40
• Can you give more hint please? I do not know how to handle the cardinality $|S|$. – Tomlin Jul 20 '18 at 6:02