Easy

Probability

Jon loves cheese. He decides to make $100$ blocks of cheese. The distribution of the weight (in grams) of each block he makes follows IID Exp$\left(\dfrac{1}{250}\right)$ distribution. Let $W_i$ denote the weight of the $i$th block of cheese, and $T_{100}$ represent the total weight of the $100$ blocks of cheese. Using Chebyshev's Inequality, what is an upper bound on $\mathbb{P}[T_{100} > 30000]$?

Notes

Hint