CS1632-Assignment 5 Full-Fledged GUI Program Solved

For this final deliverable, you will develop a full-fledged GUI program (with
the help of some skeleton code), along with various tests.  

The bean counter is a device for statistics experiments devised by English
scientist Sir Francis Galton. It consists of an upright board with evenly
spaced pegs in a triangular form.  Beans are dropped from an opening at the top
of the board. Every time a bean hits a peg, it has a 50% chance of falling to
the left or to the right.  In this way, each bean takes a random path and
eventually falls into one of the slots at the bottom of the board.  After all
the beans fall through, the number of beans in each slot is counted.

See the following link for a more detailed description of the machine:
https://en.wikipedia.org/wiki/Bean_machine.

The bean counter had two contributions to statistics by demonstrating the following:
1. When the sample size is large enough, a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) approaches a [bell curve](https://en.wikipedia.org/wiki/Normal_distribution).
2. It also demonstrated a phenomenon named [regression to the mean](https://en.wikipedia.org/wiki/Regression_toward_the_mean).

Regression to the mean had been (and still is) a source of numerous scientific
misconceptions.  People make conjectures all the time about all types of things
and provide reasons for it.

1. Why is my favorite sports team performing in a mediocre way when it won the championships last year?  Because my favorite player was traded.
2. Why did the crime rate in my city fall down to the national average?  Due to better policing.
3. Why did a student who did exceptionally well on the midterms perform just about average on the finals?  Because the student slacked off.

People always look for reasons for changes in data.  But often the reason
cannot be explained, because there was no reason for the change to begin with.
The change in data can just be due to a statistical anomaly called "regression
to the mean".  For example, an answer to question 3 can simply be that the
student was exceptionally lucky during the midterms (she guessed all multiple
choices and she got them all correct).  In the finals, her luck wore just off
and she just got what she deserved.  This is called regression to the mean.
When a data point is on the extremes of the bell curve, it is often not because
there is anything special about that data point, it is because the laws of
probability worked in favor of it (or against it, depending on context) for
that particular trial.  If that's the case, chances are that the data point
will move to the mean in the next trial.

Now if the exceptional score was due to skill, then the regression would not
happen unless there was a regression in skill.  The problem is, it is very hard
to tell whether something was due to luck or skill just by looking at the
results, hence the numerous misconceptions.