This paper evaluates exact coverage probabilities of approximate prediction intervals for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the sample. The failure-time of such units is modeled with a Weibull distribution having a given shape parameter value. We illustrate the use of the procedures by using data from a nuclear power plant heat exchanger. The results suggest that the likelihood-based prediction intervals perform better than the alternatives.