Example 8. The average germination rate of seeds is $80 \%$. Find the most probable number of germinated seeds among nine seeds.
Solution. The number $k_{0}$ will be determined using inequalities (3.1.5). Since $n=9, p=0.8$, and $q=0.2$, then $9 \cdot 0.8 - 0.2 \leq k_{0} \leq 9 \cdot 0.8 + 0.8 = 8$. An integer is obtained; hence, there are two most probable numbers of germinated seeds: 8 and 7. Their probabilities are the highest and equal to each other.

Indeed,

$$
\begin{aligned}
& P_{9}(7)=C_{9}^{7} p^{7} q^{9-7}=C_{9}^{7} \cdot(0.8)^{7} \cdot(0.2)^{2}=36 \cdot 0.2097 \cdot 0.04 \approx 0.302 \\
& P_{9}(8)=C_{9}^{8} p^{8} q^{9-8}=C_{9}^{8} \cdot(0.8)^{8} \cdot 0.2=9 \cdot 0.1678 \cdot 0.2 \approx 0.302
\end{aligned}
$$