= Solution
The root calculation for the <Huber location estimator> gives
$$
\operatorname{IF}(z;T,\Phi)=\frac{\psi_b(z)}{2\Phi(b)-1}.
$$
Since $|\psi_b(z)|\leq b$ and equality is attained for $|z|\geq b$, its <gross-error sensitivity> is
$$
\boxed{\sup_z|\operatorname{IF}(z;T,\Phi)|=\frac{b}{2\Phi(b)-1}<\infty.}
$$
Thus it is a <B-robust estimator> at the normal reference distribution. At a general centred distribution the same conclusion requires $m=\mathbb E_F\psi_b'(X)>0$, in which case the bound is $b/m$. Boundedness of the score alone does not rescue a zero sensitivity denominator.
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