Interval estimates are generally to be preferred over point estimate
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When, over a given range, the probability that a variable in question lies within a particulat interval is equal to the size of that interval as a proportion of the range.
Less time and less cost for a sample
When you have independent events which have a constant probability of occurrence over an interval of space or time.
Independent events with a constant probability of occurrence over a fixed interval of time (or space).
It can be though more often it is a variable on the interval scale (when looking for trends over time).