The best way to see the Centra

The best way to see the Central Limit Theorem at work is to use one of the Java applets that are available on the Web. There are many such applets and as of this writing one of the best can be found at http://www.maths.soton.ac.uk/ teaching/units/ma1c6/links/samplingapplet/samplingapplet .html. Use all of the options that are available at that site to produce histograms based on different-sized samples from each of the three distributions: normal, exponential, and uniform. Note how the shape of the histogram changes as the sample size changes for a given distribution. At what size sample would you say that the distribution of the sample mean appears to be approximately normal for each distribution? Do you agree with the number of classes that were used in constructing each of the histograms? If you disagree, do you believe that your conclusions about the minimum sample sizes necessary for approximate normality would have been different if a different number of classes had been used? (If for some reason this particular applet is no longer available, do the exercise on an applet that is available.)

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