Example 24. When manufacturing a certain product, its weight $X$ is subject to random fluctuations. The standard weight of the product is 30 g, its standard deviation is 0.7, and the random variable $X$ is normally distributed. Find the probability that the weight of a randomly selected product is within the range of 28 to 31 g.
Solution. We will use formula (3.5.2): In this case, $a=30$, $\sigma=0.7$, $\alpha=28$, $\beta=31$. According to the specified formula, we find

$$
\begin{gathered}
P(28<X<31)=\Phi\left(\frac{31-30}{0.7}\right)-\Phi\left(\frac{28-30}{0.7}\right)=\Phi(1.43)-\Phi(-2.86)= \\
=\Phi(1.43)+\Phi(2.86)=0.424+0.498=0.922
\end{gathered}
$$