Example 5. The germination rate of seeds of this plant is 0.9. Find the probability that out of 900 sown seeds, the number of sprouted seeds is between 790 and 830.
Solution. To find the required probability, we will use formula (4.3.7). From the condition, it follows that $n=900, k_{1}=790, k_{2}=830$, $p=0.9, q=0.1$. Using formulas (4.3.6), we determine

$$
\begin{gathered}
x_{1}=\frac{790-900 \cdot 0.9}{\sqrt{900 \cdot 0.9 \cdot 0.1}}=\frac{790-810}{\sqrt{81}}=-\frac{20}{9} \approx-2.22 \\
x_{2}=\frac{830-900 \cdot 0.9}{\sqrt{900 \cdot 0.9 \cdot 0.1}}=\frac{830-810}{\sqrt{81}}=\frac{20}{9} \approx 2.22
\end{gathered}
$$

Using the table of values of the Laplace function (see appendix), we find

$$
\Phi\left(x_{2}\right)=\Phi(2.22) \approx 0.4868 ; \quad \Phi\left(x_{1}\right)=\Phi(-2.22) \approx-0.4868
$$

According to formula (4.3.7), we obtain the required probability

$$
P_{900}(790,830)=\Phi\left(x_{2}\right)-\Phi\left(x_{1}\right)=0.4868+0.4868=0.9736
$$