Central Limit Theorem for exponential distribution Suppose that $X_1,\ldots,X_n$ are a random sample from a population having an exponential
distribution with rate parameter $\lambda$.
Use the Central Limit Theorem to show that, for large $n,$ $\sqrt{n}(\lambda\bar{x}-1) \sim \operatorname{Normal}(0,1)$
My attempt: honestly I am really not understanding what this question is asking. I can see that for an exponential distribution, it would have to be shifted by $\lambda$ and scale by a factor of $\sigma$?

The mean and variance of exponential distribution with parameter $\lambda$ are respectively $\dfrac{1}\lambda$ and $\dfrac{1}{\lambda^2}$,
so central limit theorem says
$$\sqrt{n}(\bar{x} - \frac{1}{\lambda}) \to \mathcal{N}(0,\frac{1}{\lambda^2})$$
Multiply both sides by $\lambda$ to conclude
