Open the applet,

https://media.pearsoncmg.com/cmg/pmmg_mml_shared/animations/statistics/west_applets_HTML5/popsample.html

1. Set "Select distribution" to "Bell shaped". The distribution of the population should appear as a bell-shaped curve spanning the horizontal axis (0 to 50) with a mean 25, median 25, and standard deviation 5.
2. Recall that for the uniform distribution the mean and median were also 25, but the standard deviation was 14.4309. Give a brief explanation of why the standard deviation of the uniform distribution is larger than the standard deviation of the bell-shaped curve, in this case.
3. Enter "20" into the "Sample size" box and the click the "Sample" button in the upper left corner. What is the mean of the sample?
4. Generate a new sample of 20 by clicking the "Sample" button again. What is the mean of the sample?

In both this exercise and the previous one, a sample size of 20 was used. In which case (#1 - uniform or #2 - bell shaped) did the sample means better approximate the population mean? Was this just random chance or can you think of a reason why this would happen? Explain.