Normal distribution
input the mean, standard deviation and limits (a & b) show the normal curve with shading and the probability.
Input the mean, SD, a percentage and a direction, show the normal curve with the indicated tail shaded and the value of X that corresponds to the percentage that is given.
Central Limit Theorem
Given a mean, SD, and sample size, display the normal curve associated with the underlying distribution (using the mean and SD) and the normal curve associated with the sampling distribution (using the mean with SD/sqrt(N). The sampling distribution would be the same as the underlying distribution but would be sqrt(N) times taller and 1/sqrt(N) times the width. It would be centered at the same place.
Confidence Intervals
Given a mean, SD and confidence level (CL%) display a normal distribution with the middle CI% shaded and the limits for that confidence level calculated.
Central Limit Theorem Example
Display a population of fat people along with a relative frequency histogram (the heights of the bars correspond to the percentage of individuals in each class) for the entire population. Users can indicate a sample size and click a button labeled “SAMPLE NOW”. The computer selects a sample of the appropriate size, computes its average weight and displays that average along with some symbol (like a little arrow) on the histogram indicating the location of the average. When the user clicks “SAMPLE NOW” again, a new sample is chosen and a new arrow appears on the histogram. The old arrow(s) stay on the histogram until the user clicks a button labeled “RESET” which clears all of the arrows from the histogram.
Display a population of fat people along with a relative frequency histogram (the heights of the bars correspond to the percentage of individuals in each class) for the entire population. Users can indicate a sample size and number of samples. The computer then generates the requested number of samples from the population, computes their averages and displays a relative frequency histogram of the averages superimposed on the original histogram.
In both of the above, it would be nice to be able to select among several choices for the underlying distribution for the population. This selection could be initially between a uniform (flat) distribution and a Poisson distribution, but we could add other choices (Skewed left, Skewed right, normal, bimodal, - I can help with the mathematics that descibe each of these.)
-- JohnTNoonan - 2012-07-27