Let $\mu\_{n}$ be the $\text{Uniform}(\alpha\_{n},\beta\_{n})$ probability distribution for $\alpha\_{n}< \beta\_{n}$ , $n = 1,2,3,\ldots$

What condition on these two sequences makes $\left\{\mu\_{n}\right\}\_{n}$ relatively compact?

I know that using Prokhorov's Theorem we can show conditions for tightness.

(If $\Omega$ is a complete separable metric space then a family of distributions is relatively compact if and only if it is tight.)

Using this theorem I will want to show,

$$\mu\_{n}\{[-m,m]\} > 1-\varepsilon$$

for any $\varepsilon>0$ and $m>0$.

But I don't really know how to go about doing this. Any help would be greatly appreciated!