AbstractIt is important for applied statisticians to know if data that can be described by the Weibull distribution can also be described by the normal distribution. Some investigations have been published on this subject. In this article, we review the results in papers related to the above problem. Next, we define the mean hazard rate. We then investigate the properties of the mean hazard rate for the Weibull distribution and the normal distribution, respectively. Finally, we discuss the method of approximating the normal distribution by the Weibull distribution using the mean hazard rate.