Conceptualization using a statistical JAVA applet

First, I have to give credit to the programmer (D. Lane at Rice Univ) and to E. Iversen (last term's STA110B instructor) for finding this applet. In recent lectures, we have discussed the fact that we can use the normal distribution to approximate the binomial theorem; this is particularly useful when n is large and the binomial theorem would involve many calculations. This is particularly true for large n (number of trials or sample size). The applet allows you to specify a population proportion, pi, and the sample size n. The applet can be found at http://www.ruf.rice.edu/~lane/stat_sim/binom_demo.html.

1. If n is relatively small (say n=20 or so), for what values of p does the binomial distribution appear to be closest to normal-looking? (For instance, you might try p=0.1, 0.3, 0.5, 0.7, 0.9.)
2. If the values for p are very close to 0 or 1, how big does n have to be before the distribution looks approximately normal?
3. In general (for whatever values of p), how does the size of n affect the accuracy of the normal approximation?
4. What does the above question imply about the accuracy of the normal approximation to the binomial when p is unusually large or small?

Another JAVA applet

For this example, credit goes to C. Merrill at BYU (the programmer) and E. Iversen for finding it on the web. This example is self-explanatory; it shows that the sample mean will tend to toward the population mean as the sample size gets larger. You can experiment with differently shaped distributions to see this. The applet is at http://arbitrage.byu.edu/sample.html

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