Example 13. When measuring a part, random errors occur that follow a normal distribution with the parameter $\sigma=10$ mm. Find the probability that the measurement is made with an error not exceeding $15 \mathrm{MM}$.
Solution. We will use formula (3.5.4) and the table of values of the Laplace function. In this case, $\delta=15, \sigma=10$, so

$$
P(|X-a|<15)=2 \Phi\left(\frac{15}{10}\right)=2 \Phi(1.5)=2 \cdot 0.433193=0.866386
$$