Standard deviation and probability for decay

[Flabbergast]

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

 

[kuruman]

need answers

We don't give answers, just hints. Hint: This is an application of Poisson statistics.

 

[Flabbergast]

We don't give answers, just hints. Hint: This is an application of Poisson statistics.

i know that

 

[kuruman]

i know that

Then what is it that you don't know? Please be specific.

 

[BvU]

Hi Flab,

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)

need answers

See kuruman...

Average = 0.108 $\pm$ 0.328 looks weird to me too. But the exercise asks for

the standard deviation of the counts, and therefore what is the error on your calculated value

 

[haruspex]

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.