If we know the distribution, we know everything. Feed in a distribution — pick one and draw a
sample, or paste your own — then ask any question: P(X > T) or
P(T1 ≤ X ≤ T2). The bootstrap resamples 10,000× to tell you the answer
and how sure we can be — no formulas, no distribution assumptions.
Same machine as the ratings demo: run M experiments and see how the answer spreads — but each experiment is a resample of your sample, so N is locked to your sample size. Resampling cannot invent data you didn't collect.
Method. Nonparametric bootstrap. Whatever the question, we compute the answer once on
your sample, then resample the sample with replacement (same n) and recompute it — M×.
The spread of those M answers is our uncertainty: the 95% interval is the 2.5th–97.5th percentiles.
For an event like P(X > T) the answer is the fraction of values in the event; for
P(mean > T) the statistic is the mean. Same machine, any question — no closed-form formula needed.