= Solution
The <central limit theorem> suggests approximating $S$ by a normal variable with mean $400$ and <variance> $560$. Thus
$$
\boxed{\mathbb P(S\geq500)\approx1-\Phi\left(\frac{500-400}{\sqrt{560}}\right).}
$$
Since $S$ is integer-valued, the usual <continuity correction> replaces $500$ by $499.5$:
$$
\mathbb P(S\geq500)\approx1-\Phi\left(\frac{99.5}{\sqrt{560}}\right).
$$
These are approximation formulas rather than consequences of Chebyshev's bound; the <standard deviation> is $\sqrt{560}$, not $560$.
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