This question is based on this question: How to calculate a confidence level for a Poisson distribution? and its answers.
In that post, the question is "How do I calculate the confidence interval of a poisson distribution with $n = 88$ and $\lambda =47.18$?"
The answer came as
$$ \lambda \pm 1.96\sqrt{\dfrac{\lambda}{n}}, $$
for the upper and lower bounds. It might be noted that this is an approximation which is okay when $n\lambda$ is big enough -- whatever big enough might be, apparently $4152$ is big enough.
Now, as far as I know -- this might be completely wrong since I haven't really properly studied statistics yet -- the confidence interval gives you an interval such that the probability that the mean is in this interval is $95\%$. So, I'd think the probability of being outside this interval would be $2.5\%$? But it's not. So I'm confused.