1598. The probability of manufacturing a part of the highest grade on a given machine is 0.4. Find the probability that among 26 randomly selected parts, half will be of the highest grade.
Solution. It is required to find the probability $P_{13}$ 26. Knowing the Laplace theorem, the necessary calculations are performed according to the following scheme:

$$
\begin{array}{cc}
p=0.4 ; & n p=26 \cdot 0.4=10.4 ; \\
q=1-0.4=0.6 ; & n p q=10.4 \cdot 0.6=6.24 ; \\
n=26 ; & \sqrt{n p q}=V \overline{6.24}=2.50 ; \\
m=13 ; & m-n p=13-10.4=2.6 ; \\
& x=\frac{m-n p}{\sqrt{n p q}}=\frac{2.60}{2.50}=1.04 ; \\
& \varphi(x)=\varphi(1.04)=0.2323 \\
& P_{m n} \approx \frac{\varphi(x)}{\sqrt{n p q}}=\frac{0.2323}{2.50}=0.093
\end{array}
$$

The values of the function $\varphi(x)$ are found using a table (Appendix 1). 1599. A coin was tossed 40 times. Using the local Laplace theorem, find the probability that the head will appear 25 times.