This got me thinking. Since using the Monte Carlo Method is one of my favorite methods to solve problems, it seemed that this would be a perfect problem to solve.

I greatly simplified things from a SAT scoring system. But I wrote a program that would create a random test key with a specified number of solutions, and then take a specified number of problems for a specified number of tests.

I ran this program with 3, 4, and 5 solution problems, with 100 problems per test, for 1 billion tests each ( just about the maximum my computer can reasonably handle ). I used a simple scoring system where the number of right answers for each test was the percentage of the test ( hence the 100 questions ).

What I found was that the average was 33.33%, 25%, and 20% respectively. No test, out of 3 billion runs had a perfect 100%.

Here are the Standard Distribution Curves:

Here is a final thought. I had a teacher point out that if as student gets a score that is the average +/- 1 standard deviation, they had to work for that score. If it's a high score, no problem, but if it's a low score, then the student had to actually work harder than just guessing to get a

**LOWER**score!

**Update as of 05/13/2015:**The C program, scripts, and data files used to create this entry are now available on GitHub: https://github.com/lorddoomicus/tester.

## No comments:

## Post a Comment