It can be defined as the proportion of instances where the interval surrounds the true value as assessed by long-run frequency.
The coverage probability can be defined as the proportion of instances where the interval surrounds an out-of-sample value as assessed by long-run frequency.
For example, suppose the interest is in the mean number of months that people with a particular type of cancer remain in remission following successful treatment with chemotherapy.
The construction of binomial confidence intervals is a classic example where coverage probabilities rarely equal nominal levels.
The Wilson score interval is one well-known construction based on the normal distribution.
The coverage probability is the fraction of these computed confidence intervals that include the desired but unobservable parameter value.
[2] The construction of the confidence interval ensures that the probability of finding the true parameter