Calculating Probability with Poisson Distribution: Radioactive Source Counts

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    Poisson Statistic
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Discussion Overview

The discussion revolves around calculating the probability of observing more than 110 counts in a one-minute interval from a radioactive source that averages 100 counts per minute, using the Poisson distribution. Participants explore the application of statistical concepts and methods relevant to this problem.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents a problem involving the Poisson distribution and expresses uncertainty about applying the formula due to large numbers.
  • Another participant suggests that 100 counts is a fairly large number, implying that this may influence the approach to the problem.
  • A different participant references the central limit theorem as a potential consideration for the problem and notes that the mean and variance are equal in a Poisson distribution.
  • Some participants express uncertainty about how to utilize the hints provided in the discussion.

Areas of Agreement / Disagreement

Participants express uncertainty about the application of the Poisson distribution and the hints provided, indicating that the discussion remains unresolved with no consensus on the best approach.

Contextual Notes

Participants have not fully explored the implications of using the central limit theorem in this context, and there may be limitations in understanding how to transition from Poisson to normal distribution approximations.

Silviu
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Hello! I came across this problem: A counter near a long-lived radioactive source measures an average of 100 counts per minute. What is the probability that more than 110 counts will be recorded in a given one-minute interval? I am not sure how to do it. Applying the Poisson distribution formula involves very big numbers.
 
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Hint: 100 is a fairly large number.
 
Orodruin said:
Hint: 100 is a fairly large number.
I am not sure how to use that...
 
Central limit theorem comes to mind. Also being aware that the mean and variance are equal in a Poisson is useful too.
 

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