Please read the question carefully to prevent unnecessary comments!
I know that the real value and poission distribution is getting closer and closer when $n$ is large and $p$ is small. Generally , books say that it is good to use poison when $\lambda < 7$ .
I wonder something such that there are some types of question :
On the average there are $6$ no-shows per airplane flight. If there are $10$ flights scheduled, find the prob of $4$ no-shows
Solution: If there are $6$ no-shows per airplane flight , then there are $60$ no-shows for ten flights. Hence , our $\lambda$ is $60$ $$P(4)=\frac{(60)^4e^{-60}}{4!}$$
This is a classical Poisson distribution question. However , something stuck in my mind. In the beginning , our $\lambda$ was $6$ , and it was suitable value for applying Poisson , but we used $\lambda =60 $ to apply Poisson for ten flight. My question is that if the real value and the result of Poisson get diverging for large $\lambda$ such as $\lambda > 7$ , is using $\lambda =60$ a good idea ?