Example 23. The random variable $X$ is distributed according to the normal law. The mathematical expectation $a=0$ and the standard deviation of this variable $\sigma=0.5$. Find the probability that the deviation of the random variable $X$ in absolute value will be less than one.
Solution. We will use formula (3.5.4), which when $a=0$ takes the form

$$
P(|X|<\delta)=2 \Phi\left(\frac{\delta}{\sigma}\right)
$$

Since according to the condition $a=0, \sigma=0.5, \delta=1$, then

$$
P(|X|<1)=2 \Phi\left(\frac{1}{0.5}\right)=2 \Phi(2)=2 \cdot 0.4772=0.9544
$$