"If you were to measure a sample, what would the count rate have to be for, say, 95% certainty of detection?"

A distribution of counts, were we to measure the sample a large number of times, would have a standard deviation of s_D. We need to be certain, to a degree determined by k_b, that the chance of not detecting the activity when it is really there is only b, i.e.

L_D = L_C + k_bs_D = k_as₀ + k_bs_D 

When k_a and k_b correspond to the 95% confidence level

\ L_D = 2.71 + 4.65s

where s is the standard deviation of the background counts.

If the calculated peak area is less than L_C then we must quote a limit of measurement. Otherwise we can quote the estimate uncertainty.

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