Question

a background count of 600 was recorded during a 30-minute counting time. how long should a sample be counted in order to have a 5% precision for the net counting rate, if the gross count rate is about 2000 cpm?

Answer 1

Answer: t ≈ 2,403,603

Explanation:

z = the z-score associated with the desired level of confidence (for a 5% precision, z = 1.96)

σ = the standard deviation of the background count rate (which is equal to the square root of the background count rate)

E = the desired level of precision (in this case, 5% or 0.05)

Substituting the given values, we get:

σ = sqrt(600) = 24.49

t = (1.96 * 24.49 / 0.05)^2