Proof for, Vectors sampled from $D_{(L,r)}$ have Euclidean norm at most $rsqrt{n}$ with a high probability

For any $n$-dimensional lattice $L$ and $r > 0$, a point sampled from $D_{L,r}$ has Euclidean norm at most $rsqrt{n}$ except with probability at most $2^{-2n}$ (where $r$ refers to the standard deviation of the distribution). I came across this statement in the paper On Ideal Lattices and Learning with Errors Over Rings, 2012 by Peikert, Regev, Lyubashevsky. Can someone give a proof for why it is so?