Approximate mean daily wine production

Let $X$ be the number of barrels produced in one day. The individual distribution is not given as normal. With independent identically distributed daily observations, $E(\bar X)=400$ and $\operatorname{Var}(\bar X)=70^2/50=98$ exactly. The source uses $\bar X\approx N(400,98)$ by CLT for $n=50$; normality is approximate, not established as exact.

Using that approximation, $\begin{aligned}&P(\bar X>380)\approx1\\ &{}-\Phi\left(\frac{380-400}{\sqrt{98}}\right)\\ & =0.9783241244\approx0.978.\end{aligned}$ Correlated days or a changing production process would require a different variance/model.