  We consider the existence of the integrated density of states (IDS) of the
Anderson model on the Hilbert space $\ell^2(\mathbb{Z}^d)$ as analogues to the
law of large numbers (LLN). In this work, we prove the analogues central limit
theorem (CLT) for the collection of random variables associated with the
integrated density of states for the class of test functions
$C^1_P(\mathbb{R})$, the set of all differentiable (first-order) functions on
the real line whose derivative is continuous and has at most polynomial growth.
