Standard deviation and probability for decay

AI Thread Summary
The discussion focuses on calculating the average countrate and standard deviation for radiation counts from a nuclear research reactor. The average countrate is determined to be 0.108 counts per minute, with a standard deviation calculated as 0.328. Participants clarify that this standard deviation reflects the number of events in one minute, not the standard error for the rate estimate, which should consider the sample size. The conversation also highlights the application of Poisson statistics in this context. The need for precise understanding of statistical concepts is emphasized, particularly in relation to safety procedures based on radiation levels.
Flabbergast
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Homework Statement


(b)
A nuclear research reactor produces radiation for neutron scattering measurements. A safety procedure shuts the reactor down if a radiation level monitoring detector measures more than 3 counts per minute. In a test, 156 counts are recorded during a random 24 hour interval. What is the corresponding average countrate per minute? What is the standard deviation of the counts, and therefore what is the error on your calculated value (the countrate per minute)?

(c) Estimate the probability that no counts are recorded over a random one minute interval. What is the probability that the countrate during a random one minute interval exceeds 3 counts per minute, therefore tripping the safety system?

Homework Equations


SD etc.

The Attempt at a Solution


average = 156 counts / 1440min = 0.108 counts/min
SD= sqrt(0.108)=0.328
Average = 0.108+-0.328

need answers
 
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Flabbergast said:
need answers
We don't give answers, just hints. Hint: This is an application of Poisson statistics.
 
kuruman said:
We don't give answers, just hints. Hint: This is an application of Poisson statistics.
i know that
 
Flabbergast said:
i know that
Then what is it that you don't know? Please be specific.
 
Hi Flab, :welcome:

Flabbergast said:
but countrate can't be <0 so not sure this makes sense
You're right in the first point. If you define standard deviation as the square root of the variance, there is no problem with the second: the variance is well defined and well known and you have the right formula.
(in answer to the earlier post)

Flabbergast said:
need answers
See kuruman... :rolleyes:

Average = 0.108 ##\pm## 0.328 looks weird to me too. But the exercise asks for
Flabbergast said:
the standard deviation of the counts, and therefore what is the error on your calculated value
 
Flabbergast said:
SD= sqrt(0.108)=0.328
What you have calculated here is the standard deviation for the number of events in one minute, 0.108 being the average for one minute.
This is not the standard error for the estimate of the rate. That must depend on the sample size (duration of test).

Hint: what would be the standard deviation for the number in 24 hours?

By the way, I assume the calculated standard error is not expected to feature in the remaining parts of the question. If it were it seems to me you'd need to use Bayesian analysis.
 
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