On an extreme two-point distribution

A bound for functional $\mathrm{\Delta }(F)={\sup }_{x\in \mathbb{R}}\mathrm{\mid }F(x)-\mathrm{\Phi }(x)\mathrm{\mid }$ is obtained, which is uniform for all distribution functions $F$ of random variables with zero mean-value and unity variance. Moreover, a two-point distribution is found, for which this bound is reached.