Abstract: Lognormal Distribution is widely used in scientific investigation. Rao and D’Cunha (2016) reported that the Bayes credible intervals are also confidence intervals when the sample size is moderate to large. In this paper we have investigated whether the same conclusion holds for the censored data under random censoring. Extensive Monte Carlo simulation indicates that the result does not hold under random censoring. Leukemia free survival time for Allogeneic transplant patients reported in Klein and Moeschberger (2003) is reanalyzed and the results indicate that Bayes estimate of the median survival time is close to the Kaplan Meier estimator.