Solution. In this case, $M(X)=a=1000 \cdot 0.75=750$, the boundary values of the random variable $X$ are symmetric relative to $M(X)=750$. Therefore, from the original inequalities $700 \leq X \leq 800$, we can transition to the inequalities $-50 \leq X-750 \leq 50$, or $|X-a| \leq 50$, which gives the left part of inequality (4.1.4.) with $\varepsilon=50$. The value of $D(X)$ will be found using the formula $D(X)=n p q$, or $D(X)=1000 \cdot 0.75 \cdot 0.25=750 / 4$. Taking into account that $\varepsilon^{2}=50^{2}=2500$, we obtain the right part of inequality (4.1.4.):

$$
1-\frac{D(X)}{\varepsilon^{2}}=1-\frac{750}{4 \cdot 2500}=1-0.075=0.925
$$

Therefore,

$$
P(|X-750| \leq 50) \geq 0.925
$$
Example 9. The germination rate of seeds of a certain crop is 0.75. Estimate the probability that out of 1000 sown seeds, the number of seeds that will germinate will be from 700 to 800 inclusive.