Suppose $\sqrt{n}(X_n - \mu)\overset{d}{\longrightarrow}N\left(0,\sigma^2\right)$. Prove that $X_n \overset{p}{\longrightarrow}\mu$ is true.
I see that it's not true in general and I can construct a few examples when convergence in distribution does not imply convergence with probability one. But how to approach this problem?