328. The expected value and standard deviation of a normally distributed random variable $X$ are 10 and 2, respectively. Find the probability that in the experiment, $X$ will take a value in the interval $(12,14)$.
Solution. We will use the formula

$$
P(\alpha<X<\beta)=\Phi\left(\frac{\beta-a}{\sigma}\right)-\Phi\left(\frac{\alpha-a}{\sigma}\right)
$$

Substituting $\alpha=12, \beta=14, a=10$ and $\sigma=2$, we get $P(12<X<14)=$ $=\Phi(2)-\Phi(1)$. From the table in Appendix 2, we find: $\Phi(2)=0.4772$, $\Phi(1)=0.3413$. The desired probability $P(12<X<14)=0.1359$.