Example 21. The random variable $X$ is distributed according to the normal law. The mathematical expectation and variance of this variable are 7 and 16, respectively. Find the probability that the deviation of the variable $X$ from its mathematical expectation in absolute value does not exceed two.
Solution. According to the condition $M(X)=7, D(X)=16, \sigma=\sqrt{16}=4, \delta=2$. In accordance with formula (3.5.4) we find

$$
P(|X-7| \leq 2)=2 \Phi\left(\frac{2}{4}\right)=2 \cdot \Phi(0.5)=2 \cdot 0.1915=0.3830
$$