Urgent! Please take this challenge! :( statistics counting rate and standard deviation (stn or std)?

Please, I beg for your help!





I believe you must be good enough to calculate this:


an experimenter measures 9934 counts during one hour from a radioactive sample. From this number the counting rate of the sample can be estimated with a standard deviation of most nearly





a. 100 b. 200 c. 300 d. 400 e. 500





Thank you for demonstrating your ability

Urgent! Please take this challenge! :( statistics counting rate and standard deviation (stn or std)?
No, it's answer a, 100.





Radioactive emissions follow a Poisson distribution. The mean of this Poisson distribution is approximately 9934 (the observed count).





For the Poisson, the variance equals the mean, so our estimate of the variance is also 9934. The standard deviation is the square root of the variance, so our estimate here would be 99.7 which is approximately 100.
Reply:a 100
Reply:b. 200
Reply:Stat Bean has already answered this. He deserves the points, I'm just reiterating and embellishing.





Radio active counts are modelled using a Poisson distribution - the most common distribution used for arrival rates.





As he pointed out, the variance for the Poisson distribution equals mean arrival rate (λ). Standard deviation is the square root of the variance: sqrt(λ).


In your case, λ is 9934. Sqrt(9934) = 99.67 approximately equals 100.





The thing that is odd to me is that this problem was expressed in counts per hour and from what I can find, radioactivity is more frequently represented in counts per minute. Fortunately the time units don't change the math.
Reply:I am not sure, but I believe to remember it is the squair root of 9934, so it could be a) 100

wallflower