Abstract
The Uniform distribution on the interval (0, 1) plays an important role in many statistical applications, such as, its role in simulation procedures when a sequence of random numbers needs to be generated from some parent population. This paper investigates the sampling distribution of the sample mean for random samples drawn from a uniform (0, 1) population. A complete derivation of the probability density function of the sample mean is presented. The normal approximation to the series form of the probability density function of the sample mean is also discussed. To avoid the use of the complicated series form of the probability density function of the sample mean for small sample sizes when the normal approximation is not advisable, the tables of the cumulative distribution function for sample sizes 2, 3, 4 and 5 are constructed. The Minitab statistical software is used throughout this paper