# How to prove the inequality $\frac{4^m}{4\sqrt{m}}\le\binom{2m}{m}$ using chebyshev inequality [duplicate]

What is a good approach to proving this inequality:

$$\dfrac{4^m}{4\sqrt{m}}\le\binom{2m}{m}$$

using the Chebyshev inequality: https://en.wikipedia.org/wiki/Chebyshev's_inequality

I thought about using a random variable which has a binomial distribution, but im not sure.

Thank you!

EDIT: It is important to solve it only using Chebychev inequality