337. A random variable $X$ is normally distributed with a mean of $a=10$. The probability of $X$ falling in the interval $(10,20)$ is 0.3. What is the probability of $X$ falling in the interval $(0,10)$?
Solution. Since the normal curve is symmetric about the line $x=a=10$, the areas bounded above by the normal curve and below by the intervals (0,10) and (10,20) are equal to each other. Since these areas are numerically equal to the probabilities of $X$ falling into the corresponding interval, then

$$
P(0<X<10)=P(10<X<20)=0.3
$$