i got to the point(its correct) that : $\hat{\theta}_{mm}$ = $\frac{1}{\bar{X}}$
$Var(\hat{\theta}_{mm})$ = $\frac{\bar{X}-1}{\bar{X}^3}$
now I need to construct the Confidence Interval for a given $\alpha$.
i get that I need to use Asymptotic Normality but I don't get why in the solutions they divide by $\sqrt{n}$ :

