Example 17. When shooting at a target, the probability of hitting the target with one shot is 0.7. For what number of shots is the most probable number of hits equal to 16?
Solution. We refer to formula (3.1.5). In this case, $p=0.7$, $q=0.3$, $k_{0}=16$; the number $n$ is unknown and needs to be found. Formula $(3.1 .5)$ takes the form

$$
0.7 n-0.3 \leq 16 \leq 0.7 n+0.7
$$

From these inequalities, it follows that

$$
\begin{aligned}
& 0.7 n \leq 16.3, \quad 7 n \leq 163, \quad n \leq 23 \frac{2}{7} \\
& 0.7 n \geq 15.3, \quad 7 n \geq 153, \quad n \geq 21 \frac{6}{7}
\end{aligned}
$$

Thus, $n_{1}=22$ and $n_{2}=23$, i.e., the total number of shots here can be 22 or 23.