Normalized means that

$\begin{align*}\int_{-\infty}^{\infty} \left|\psi_i\left(x\right)\right|^2 = 1\end{align*}$

Orthogonal means that for $i \neq j$ ,

$\begin{align*}\int_{-\infty}^{\infty} \psi_i\left(x\right)^*\psi_j\left(x\right) = 0\end{align*}$

(E) is equivalent to these two statements combined. Therefore, answer (E) is correct.

Solution to 2008 Problem 25