An organization has an opening for a position with requirements met only met by $10$% of all applicants. Let $X$ denote the number of applicants until the position is filled. (applications are processed one at a time)
What is the probability distribution of $X$ ? And what is the mean and the variance ?
Is it normal ?
$X$ here is distributed geometrically. In fact $X$~$Geo(0.1)$. The mean of a gemetric is given by $\frac{1}{p}=\frac{1}{0.1}=10$ in this case and the variance is given by $\frac{1-p}{p^2}=\frac{0.9}{0.1^2}=90$.