334. A machine manufactures balls. A ball is considered suitable if the deviation $X$ of the ball's diameter from the design size in absolute value is less than 0.7 mm. Assuming that the random variable $X$ is normally distributed with a standard deviation $\sigma=0.4$ mm, find how many suitable balls on average will be among a hundred manufactured.
Solution. Since $X$ is the deviation (of the diameter of the ball from the design size), then $M(X)=a=0$.

Let's use the formula $P(|X|<\delta)=2 \Phi(\delta / \sigma)$. Substituting $\delta=0.7, \sigma=0.4$, we get

$$
P(|X|<0.7)=2 \Phi\left(\frac{0.7}{0.4}\right)=2 \Phi(1.75)=2 \cdot 0.4599=0.92
$$

Thus, the probability of a deviation less than 0.7 mm is 0.92. From this, it follows that approximately 92 out of 100 balls will be suitable.