This animation, created using MATLAB, illustrates how the sampling distribution of xbar is not necessarily normally distributed with mean equal to the mean of the population and the standard deviation equal to the standard deviation of the population divided by square root of n. Normality would follow from the Central Limit Theorem if the sample size is sufficiently large (here it is not since n is only 9).
xbar is not always normally distributed, so one must take caution when concluding that it is. Under these circumstances in this video, xbar is NOT normally distributed.
