Example 5. The random variable $X$ has a variance $D(X)=0.004$. Find the probability that the random variable $X$ differs from $M(X)$ by more than 0.2.
Solution. According to inequality (4.1.3), we get

$$
P(|X-a|>0.2)<\frac{0.004}{(0.2)^{2}}=\frac{0.004}{0.04}=0.1
$$