# Finding the minimum pass point

• kent davidge
In summary, a factory is hiring ##m## employees and a number ##n > m## of candidates applied to the job. They need to answer an exam consisting of questions all of equal weight. A candidate is selected to the next step (the interview) if he/she achieves a minimum of ##c## points in the exam, but as ##n > m## only those candidates with more points will be selected. If a candidate does not achieve the minimum required points, then he or she is selected for the interview.

## Homework Statement

A factory is hiring ##m## employees. A number ##n > m## of candidates applied to the job. They need to answer an exam consisting of questions all of equal weight. A candidate is selected to the next step (the interview) if he/she achieves a minimum of ##c## points in the exam, but as ##n > m## only those candidates with more points will be selected.

What, on average, is the minimum of points a given candidate must achieve in the exam in order to go to the next step?

## The Attempt at a Solution

Sorry if this is poor written. It was originally in my native language and I translated it to English, and I don't know much of English. (Using Google Translator gives a worse translation, believe...)

I tried to solve this problem by taking mean average. If there are ##n## candidates and the minimum to be considered as able is ##c##, then suppose each one of the ##n## achieves this miminum. This gives a total of ##c \cdot n## points. Now I divided this by the total number of candidates the factory is going to hire ##c \cdot n / m##. Is this the answer?

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kent davidge said:
What, on average, is the minimum of points a given candidate must achieve in the exam in order to go to the next step?
It doesn't seem like there is enough information to answer the question. Is that the whole problem statement? What is the maximum number of points on the exam? Can you assume a Gaussian distribution for the exam results?

berkeman said:
It doesn't seem like there is enough information to answer the question. Is that the whole problem statement? What is the maximum number of points on the exam? Can you assume a Gaussian distribution for the exam results?
Yes, the problem gives permission to use any method to achieve the answer, and that should include Gaussian distribution. Also, it does give explicit numbers. The minimum of points to be selected to next phase is ##60## and the maximum of points one can achieve in the exam is ##100## points.

kent davidge said:
The minimum of points to be selected to next phase is 60
So then that is the answer to the question you asked in post #1?

It seems more like they would want you to assume a mean (call it 50) and a Gaussian distribution of the n applicants, and have you figure out what the score is that has m of them passing. But I guess I'm not understanding the problem statement very well...

berkeman said:
So then that is the answer to the question you asked in post #1?
Not really
berkeman said:
It seems more like they would want you to assume a mean (call it 50) and a Gaussian distribution of the n applicants, and have you figure out what the score is that has m of them passing. But I guess I'm not understanding the problem statement very well...
I know what it asks, but in my language, not in yours. I will try again:

Because there are too much candidates, then some of them will not be selected to the next phase. The factory will select them for the interview from the one who has the max points down, until it reaches the ##m##. That is, the factory will pick the ##m## candidates who have the most quantity of points.

The problem then asks what is the average quantity of points a candidate needs to have so that he/she is within the ##m## candidates selected.

It seems to me that additional parameters need to be defined. What should also also come into play would be the mean μ and the standard deviation σ, both needed for the Gaussian. Then perhaps one can solve an equation (numerically) involving the erfc function.
http://mathworld.wolfram.com/Erfc.html

berkeman