How do I find the time?? Poisson Distribution?

Question

If the background countrate is 1 per second and the countrate with the beta source present is only 3 per second, how long would you have to measure the background counts and how long would you have to measure the beta source counts in order to have 1% precision in the difference between the two countrates? x=3...P(m)=((x^m)/m!)(e^-x)

Answer 1

for a random variable the error is the sqrt(n)/n and to have 1% difference each must have an error of .5% so 1/sqrt(n)=.005 therefore n=1/.005^2=40000
to get n counts you must measure for n sec back ground and n/3 sec for beta