Using recent results on higher order cumulants of conserved charge fluctuations from lattice QCD, we construct mean, variance, skewness, kurtosis, hyper-skewness and hyper-kurtosis net-baryon number distributions for small baryon chemical potentials $\mu_B$. For the strangeness neutral case ($\mu_S=0$) at fixed ratio electric to density ($\frac{n_Q}{n_B}=0.4$), which is appropriate a comparison...