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Binomial distribution

  1. Jul 27, 2013 #1
    1. The problem statement, all variables and given/known data
    In a class with 20 and one with 10 students each student has a probability of 0.3 to not show up on a particular day. On a given day, which class is most likely to have the highest ratio of absent students? This was in my exam, unfortunately I did not know how to do it.

    2. Relevant equations
    The probability that n students are absent on a given day in one class is binomially distributed.
    I heard some say that since the relative standard deviation goes like 1/√N the class with fewer pupils is most likely to have most absent, but I am not sure about this.

    3. The attempt at a solution
    You could do a whole lot of counting, but I don't think that's the point. Besides it would be a very tedious proces. I did it with a class of 1 and 2 students and counting even then took time.
     
  2. jcsd
  3. Jul 27, 2013 #2

    tiny-tim

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    hi aaaa202! :smile:

    (i haven't actually tried this :redface:, but …)

    i think i'd calculate Pk, the probability that exactly k students out of 30 are absent

    and then for each k the probability Qk that less than one third of k from 30 come from the 10

    (and then multiply and add)
     
  4. Jul 27, 2013 #3

    pasmith

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    Let N be the number of students absent from the large class, and M the number of students absent from the small class. The ratio of absent students will be larger for the large class if N > 2M, equal if N = 2M, and smaller if N < 2M. So you need to work out the probabilities of those three events.
     
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