  We compute analytically the distributions of concurrence $\bm{\mathcal{C}}$
and squared norm $\bm{\mathcal{N}}$ for the production of electronic
entanglement in a chaotic quantum dot. The dot is connected to the external
world via one ideal and one partially transparent lead, characterized by the
opacity $\gamma$. The average concurrence increases with $\gamma$ while the
average squared norm of the entangled state decreases, making it less likely to
be detected. When a minimal detectable norm $\bm{\mathcal{N}}_0$ is required,
the average concurrence is maximal for an optimal value of the opacity
$\gamma^\star(\bm{\mathcal{N}}_0)$ which is explicitly computed as a function
of $\bm{\mathcal{N}}_0$. If $\bm{\mathcal{N}}_0$ is larger than the critical
value $\bm{\mathcal{N}}_0^\star\simeq 0.3693\dots$, the average entanglement
production is maximal for the completely ideal case, a direct consequence of an
interesting bifurcation effect.
