A confidence interval is a range computed from data that, under repeated sampling, would contain the true value of a parameter a stated share of the time. It expresses the uncertainty of an estimate, not the spread of outcomes.
Intervals narrow as the cohort grows. A median duration estimated from a small cohort has a wide interval, and the sufficiency floor is set so that intervals are not uselessly wide.
Confusing an interval with a band is a common error. The interval describes how well the median is known. The band describes how far individual matters range around it.
A confidence interval is not a probability that the true value lies inside it for the particular interval computed.
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