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A counting question

  1. Sep 12, 2004 #1
    dear reader,
    here is a quick counting question:
    A counter near a long-lived radioactive source measures an average of 100 counts per minute. The probabilty that more than 110 counts will be recorded in a given one-minute interval is most nearly
    (A) zero
    (B) .001
    (C) .025
    (D) .15
    (E) .5
    I kinda guess that it is D, .15, but I am not able to explain it accurately, other than it is within one standard deviation. :confused:
     
  2. jcsd
  3. Sep 12, 2004 #2
    Your questions says nothing about the distribution of the counts/minute so technically, the answer could be anything.
     
  4. Sep 13, 2004 #3

    ehild

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    This should be Poisson distribution and Poisson distribution can be approximated with Gaussian one of the same mean and standard deviation if the number of counts is high. P(n>110) = 1-F(110), where F is the probability distribution function. To calculate with the normalized Gaussian distribution, you transform the variable n (number of counts) to u=(110-100)/10=1,

    [tex]F(110)=\Phi(1)[/tex],

    From a table for normalized Gaussian distribution [tex]\Phi (1) = 0.8413 [/tex], so the probability of getting a count number greater than 110 is 1-0.8413=0.1587. So your answer seems to be all right.


    ehild
     
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