PLOT A VARIABLE WITH NORMAL DISTRIBUTION WITH MEAN 200 AND DEVIATION 20. SUPERIMPOSED WITH THE PREVIOUS FIGURE, PLOT THE DISTRIBUTION OF THE ARITHMETIC MEAN OF SAMPLES OF SIZE N=4, 25 AND 100, OF THAT POPULATION?

A normal distribution with a mean of 200 and a deviation of 20 can be plotted as a bell-shaped curve, as shown in the figure below.

Superimposed on the figure, the distribution of the arithmetic mean of samples of size n=4, 25 and 100 can be plotted as shown in the figure below. The arithmetic mean distribution for n=4 is a much narrower distribution than a normal distribution, since it is based on a small sample size. As the sample size increases, the distribution becomes wider and more similar to the normal distribution.