A count total without a measurement model

A fictional radiation measurement exercise records 400 counts during a specified counting interval. It explicitly asks only for the standard deviation of that gross count under a Poisson model. A separate background measurement exists, but the question does not ask for a net count, dose or activity conversion. One learner reports an uncertainty of twenty counts, while another claims this proves the detector is correctly calibrated and the measured person dose is safe. The tutor asks students to separate the narrow statistical calculation from conclusions requiring geometry, detector efficiency, background treatment and a protection assessment. No actual exposure limit, medical assessment or release decision is supplied in this conceptual problem.