  We have investigated how uncertainties in the estimation of the detection
efficiency affect the 90% confidence intervals in the unified approach for
constructing confidence intervals. The study has been conducted for experiments
where the number of detected events is large and can be described by a Gaussian
probability density function. We also assume the detection efficiency has a
Gaussian probability density and study the range of the relative uncertainties
$\sigma_\epsilon$ between 0 and 30%. We find that the confidence intervals
provide proper coverage over a wide signal range and increase smoothly and
continuously from the intervals that ignore scale uncertainties with a
quadratic dependence on $\sigma_\epsilon$.
