Data obtained in biomedical research is often skewed. Examples include the incubation period of diseases like HIV/AIDS and the survival times of cancer patients. Such data, especially when they are positive and skewed, is often modeled by the log-normal distribution. If this model holds, then the log transformation produces a normal distribution. We consider the problem of constructing confidence intervals for the mean of the log-normal distribution. Several methods for doing this are known, including at least one estimator that performed better than Coxxs method for small sample sizes. We also construct a modified version of Coxxs method. Using simulation, we show that, when the sample size exceeds 30, it leads to confidence intervals that have good overall properties and are better than Coxxs method. More precisely, the actual coverage probability of our method is closer to the nominal coverage probability than is the case with Coxxs method. In addition, the new method is computationally much simpler than other well-known methods.