Problem:
A recruiting firm finds that $20$% of the applicants for a particular sales position are fluent in both English and Spanish. Applicants are selected at random from the pool and interviewed sequentially.
Suppose that the first applicant who is fluent in both English and Spanish is offered the position, and the applicant accepts. Suppose each interview costs $ \$125$. The expected value and standard deviation of the cost of interviewing until the job is filled. are, respectively :
So I applied
$\sum_{i=1}^{\infty}ip(1−p)^{i−1} = \frac{1}{p}$
and got $\frac{1}{0.2} = 5$ meaning expected number of interviews is $5$.
So I think the expected value of this is $5*125 = 625$.
I am stuck here and don't know what to do next. Maybe I did things completely wrong and should have used some Poisson random variable things?
Can you give me some ideas on what to do?
Thank you in advance!