  We compute the probability distribution $P(N)$ of the net-baryon number at
finite temperature and quark-chemical potential, $\mu$, at a physical value of
the pion mass in the quark-meson model within the functional renormalization
group scheme. For $\mu/T<1$, the model exhibits the chiral crossover transition
which belongs to the universality class of the $O(4)$ spin system in three
dimensions. We explore the influence of the chiral crossover transition on the
properties of the net baryon number probability distribution, $P(N)$. By
considering ratios of $P(N)$ to the Skellam function, with the same mean and
variance, we unravel the characteristic features of the distribution that are
related to $O(4)$ criticality at the chiral crossover transition. We explore
the corresponding ratios for data obtained at RHIC by the STAR Collaboration
and discuss their implications. We also examine $O(4)$ criticality in the
context of binomial and negative-binomial distributions for the net proton
number.
