Calculating Probability with Poisson Distribution: Radioactive Source Counts

In summary, the conversation discusses the probability of recording more than 110 counts in a one-minute interval when the average count is 100 counts per minute. The use of the Poisson distribution formula, the central limit theorem, and the equal mean and variance in a Poisson distribution are mentioned as potential approaches to solving the problem. A resource for converting from a Poisson to a normal distribution is also provided.
  • #1
Silviu
624
11
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.
 
Physics news on Phys.org
  • #2
Hint: 100 is a fairly large number.
 
  • #3
Orodruin said:
Hint: 100 is a fairly large number.
I am not sure how to use that...
 
  • #4
Central limit theorem comes to mind. Also being aware that the mean and variance are equal in a Poisson is useful too.
 

1. What is the Poisson distribution?

The Poisson distribution is a probability distribution that is used to model the number of events that occur in a fixed interval of time or space. It is often used to analyze rare events or situations where events occur independently of each other.

2. What are the assumptions of the Poisson distribution?

The Poisson distribution assumes that the events occur at a constant rate, events occur independently of each other, and the probability of an event occurring in a given interval is proportional to the length of the interval.

3. How is the Poisson distribution different from other probability distributions?

The Poisson distribution is different from other distributions, such as the normal distribution, because it is a discrete distribution, meaning that the possible outcomes are countable and not continuous. It also only has one parameter, the rate parameter, whereas other distributions may have multiple parameters.

4. How is the Poisson distribution used in real-world applications?

The Poisson distribution is commonly used in areas such as insurance, finance, and healthcare to model the number of rare events, such as accidents, defaults, or medical emergencies. It is also used in quality control to monitor defects in a production process.

5. How can the Poisson distribution be applied in research studies?

The Poisson distribution can be used to analyze data from studies that involve counting the number of occurrences of a certain event, such as the number of bacteria in a sample or the number of mutations in a gene. It can also be used to test the significance of observed frequencies in comparison to expected frequencies.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
12
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
21
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
4K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
348
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
2K
Back
Top