Chebyshev bound on total weight of 100 cheese blocks

A cheesemaker produces $100$ blocks. Their weights $W_1,\dots,W_{100}$ (in grams) are independent, each exponential with rate $\tfrac{1}{250}$ (so mean $250$ g). Write $T_{100}=W_1+\dots+W_{100}$ for the combined weight. Apply Chebyshev's inequality to obtain an upper bound for $\mathbb{P}[T_{100}>30000]$.

$1/4$. $T_{100}$ has mean $25000$ and variance $100\cdot 250^2$. The event $T_{100}>30000$ is contained in $|T_{100}-25000|>5000$, so Chebyshev gives at most $\tfrac{100\cdot250^2}{5000^2}=\tfrac14$.