A long-half-life sealed source gives counts 47, 54, 50, 43 and 56 in five consecutive 5.0 s intervals with unchanged detector geometry and settings. Background is 0.80 counts s⁻¹. Calculate the mean corrected source rate, explain what the variations imply, and name two controls needed to rule out non-random causes. Would the next 5.0 s count necessarily equal the mean?

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Mean measured count 50; corrected rate 9.2 s⁻¹. Variations support random decay, given constant conditions; the next count is not fixed. Total counts = 250 in 25.0 s, so measured mean rate = 10.0 s⁻¹. Subtract background: source rate = 10.0 − 0.80 = 9.2 s⁻¹. Equal-duration fluctuations with negligible expected activity change indicate unpredictability of individual decay events. Controls include fixed source-detector separation/orientation, identical intervals and unchanged detector settings. No: the mean describes the expected rate of many observations, not a guaranteed next count.

Infer randomness from count data

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