#central-limit-theorem

Question 1: Single choice

For $X \sim \textrm{Poisson}(\lambda)$ , $(X - \lambda)/\sqrt{\lambda}$ is approximately standard normal when $\lambda$ is large. Why does this make sense?

For integer $\lambda$ , $X$ is a sum of $\lambda$ independent $\textrm{Poisson}(1)$ variables, so the central limit theorem applies1
The Poisson mass function equals the Gaussian density exactly once $\lambda$ is large enough2
Subtracting the mean and dividing by the standard deviation always turns a variable into a standard normal3
The Poisson is the limit of binomials, and every binomial is Gaussian when $p$ is small4

#central-limit-theorem

Timed test