Separate a binomial mean approximation from its exact total

$\mu=9(0.5)=4.5$ and $\sigma^2=9(0.5)(0.5)=2.25$. For 60 independent observations, the source uses $\bar X\approx N(4.5,2.25/60)=N(4.5,0.0375)$ by CLT. Thus $\begin{aligned}&P(\bar X>5)\approx1\\ &{}-\Phi\left(\frac{0.5}{\sqrt{0.0375}}\right)\\ & =0.0049116373\approx0.00491.\end{aligned}$

The total $T=60\bar X\sim B(540,0.5)$ exactly under the independent binomial model. The strict event is $T>300$, hence $T\ge301$. Its exact probability is 0.004301767220. This is an additional check, not the printed CLT result; unadjusted continuous approximation and exact discrete tail differ.