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Exercise on Poisson distribution

  1. Sep 4, 2015 #1
    1. The problem statement, all variables and given/known data

    An experimenter measures the counting rate from a radioactive source as 10,150 counts in 100 minutes. Without changing any of the conditions, the experimenter counts for one minute. There is a probability of about 15 percent that the number of counts recorded will be fewer than

    (A) 50
    (B) 70
    (C) 90
    (D) 100
    (E) 110

    2. Relevant equations

    Poisson distribution: ##P(\nu) = e^{-\mu}\frac{\mu^{\nu}}{\nu!}##, where ##\mu## is the mean and ##\nu## is the number of events for which the probability is to be calculated, both values taken over a definite interval.

    3. The attempt at a solution

    The first step is to find the average in 1 minute, and that is 10,150/100 = 101.50.

    Now, do I have to figure out the probability for each of 101.5, 100, 99, ... , to figure out the answer, or is there an easy way?
     
  2. jcsd
  3. Sep 4, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You can use the cumulative distribution.
    Alternatively, make a rough estimate for the probabilities. What is the standard deviation of the count rate?
    There is one correct answer, the others can be ruled out without detailed calculations.
     
  4. Sep 4, 2015 #3
    I don't know how to calculate the standard deviation for this Poisson distribution. Could you please help me?
     
  5. Sep 4, 2015 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Google 'Poisson distribution'.
     
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