Normal functors and paranormality

It is proved that if $\mathcal{F}\colon\mathcal{P}\longrightarrow\mathcal{P}$ is a normal functor of degree $\geqslant 3$ in the category $\mathcal{P}$ of paracompact $p$-spaces and perfect mappings, and the space $\mathcal{F}(X)$ is hereditarily paranormal, then the space $X$ is metrizable.