Task 1. The probability of event $A$ occurring in each of 484 independent trials is 0.75. Find the probability that the relative frequency of event $A$ deviates from its probability in absolute value by no more than 0.03.
Solution. Given: $n=484 ; p=0.75 ; q=0.25 ; \varepsilon=0.03$. By formula (27) we have:

$$
\begin{aligned}
& P\left(\left|\frac{m}{n}-0.75\right|<0.03\right) \approx 2 \Phi\left(0.03 \sqrt{\frac{484}{0.75 \cdot 0.25}}\right)=2 \Phi(1.524)=0.872 \\
& \text { Answer. } 0.872
\end{aligned}
$$