A famous application involving the number $e$ comes from Optimal Stopping theory. Known as the Best Choice Problem, it concerns hiring someone for a job under the following conditions:

• You have $n$ people to interview.
• You interview them one-by-one.
• After each person is interviewed, you must immediately make the decision of whether to hire them or not. If you hire them, you’re done and you cannot interview anymore candidates.
• If you reject a candidate (decide not to hire them), you can’t change your mind later.

Under these conditions, you may wonder how to actually choose the best person for the job. If you choose a good candidate early on, you may miss the opportunity to hire a really great candidate later down the line. If you wait too long, you may only be left with mediocre candidates from which to choose. The solution is to interview the first $\frac{n}{e}$ candidates but reject all of them, regardless of their qualifications. Then, continue interviewing candidates until you find the first one that is “better” than the first group you rejected. Hire this person. Interestingly, this simple rule has been shown to find the best candidate in a group approximately $37 \%$ of the time, no matter the size of the group! Question: Suppose a group of people line up to be chosen as an extra in a movie. The casting director only has time to interview people one at a time and make a decision: yes or no. Suppose the casting director is familiar with the Best Choice Problem, and she interviews and rejects the first $15$ people in line. How many people are in line? Round your answer to the closest whole number. Answer: There were total people.