126. A substance is being weighed without systematic errors. Random errors $X$ in weighing are subject to a normal distribution with a root mean square deviation $\sigma=20$ g. Find the probability that the weighing will be performed with an error not exceeding $10 \mathrm{r}$ in absolute value.
S o l u t i o n. The random variable $X$ - random weighing errors. The expected value of $X$ is $a=0$. The required probability will be found using formula (63) with $\varepsilon=10$:

$$
P(|X-0| \leq 10)=2 \Phi(10 / 20)=2 \Phi(0.5)
$$

From the table of values of the function $\Phi(x)$ (see table 3 in the appendix), we find $\Phi(0.5)=0.1915$. Substituting the value of $\Phi(0.5)$ into formula (*), we find $P(|X| \leq 10)=0.383$.