Problem 6. The probability of a shooter hitting the target is 0.5. Find the probability that the target will be hit from 5 to 7 times inclusive out of 8 shots.
Solution. By formula (20) we have:

$$
\begin{aligned}
& p_{8}(5 \leqslant k \leqslant 7)=p_{8}(5)+p_{8}(6)+p_{8}(7)= \\
& \quad=C_{8}^{5} \cdot p^{5} \cdot q^{3}+C_{8}^{6} \cdot p^{6} \cdot q^{2}+C_{8}^{7} \cdot p^{7} \cdot q=\frac{23}{64} \approx 0.3534
\end{aligned}
$$

Answer. $0.3534$.