Conclusions

After experimentation and data analysis, it was also found that having 20 questions on the exam is crucial in preventing flukes. With 10 questions on the exam, many students can pass the exam without any knowledge whatsoever!

From left to right, the general probability distribution goes up, peaks at around 20% of a perfect score, and drops down. It is nearly impossible to get a perfect score, but it is quite possible in getting a score of 0. The chances of getting a passing mark are quite slim, depending on the scenario. Using statistical calculations, the expected class average is 25%.

The data absolutely supported 20 questions, while it only supported 5 answer choices slightly more than 4 answer choices. For the second part of the second hypothesis, I was correct in stating that obtaining 100% would be the hardest. However for the first part, I was incorrect. I hypothesized that the most probable score would be 35% which is much higher than the result: 25%. The data supported my third hypothesis and it is correct. The chance of passing is 0.4155%... extremely slim indeed! Lastly, I was incorrect about the class average. My hypothesis of 40% was much higher than the result which was 25%.

Using the theory of probability, the theoretical chance of obtaining a perfect score (with 20 questions and 4 answer choices) is! This means 1 in 1 099 511 627 776! No one on Earth will be able to get a perfect score!! Truly, one should not purely guess on the answers of a multiple choice exam.