Undergrad Calculating Probability with Poisson Distribution: Radioactive Source Counts

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To calculate the probability of recording more than 110 counts in a minute from a radioactive source with an average of 100 counts per minute, the Poisson distribution can be applied. Given that 100 is a large number, the central limit theorem suggests that the distribution can be approximated by a normal distribution. The mean and variance being equal in a Poisson distribution simplifies calculations. Using these principles, one can derive the probability without dealing with excessively large numbers. Understanding these concepts is crucial for solving the problem effectively.
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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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