# Estimating Poisson-distributed rate using sampling

You have been hired by the border patrol agency of a nation to estimate the number of people who enter into the country by circumventing the fence during their busiest season. You have reason to believe the rate at which these people come follows a Poisson distributionThe border consists primarily of flatland. You and your assistant spend 3 days underground tallying all the people within your 3-mile field of view who circumvent the fence. Over the course of those days, you see an average of 64 people.

What is your 95% confidence interval?

I may be a layman, but it looks like I could try treating this as a T-test. What do you suggest I do?

The variance of a possion is equal to its mean $\mu$, you can use $\bar{X}\pm 1.96\sqrt{\bar{X}}$ to estimate your 95% CI of $\mu$ which is $64 \pm 1.96\sqrt{64}$ for 3 days and 3-mile field, you also can estimate 1 day and 1-mile 95% CI by dividing the interval by 9.