120. Find the probability that event $A$ will occur 1400 times in 2400 trials, if the probability of this event occurring in each trial is 0.6.
Solution. Since $\boldsymbol{n}$ is large, we will use the local Laplace theorem:

$$
P_{n}(k)=\frac{1}{\sqrt{n q p}} \varphi(x)
$$

Let's calculate $x:$

$$
x=\frac{k-n p}{\sqrt{n p q}}=\frac{1400-2400 \cdot 0,6}{\sqrt{2400 \cdot 0,6 \cdot 0,4}}=-\frac{40}{24}=-1,67
$$

The function $\varphi(x)=\frac{1}{\sqrt{2 \pi}} e^{-x^{2} / 2}$ is even, so $\varphi(-1,67)=\varphi(1,67)$.

From the table in Appendix 1, we find $\varphi(1,67)=0,0989$.

The desired probability

$$
P_{2400}(1400)=1 / 24 \cdot 0,0989=0,0041 .
$$