In a test with 100 multiple choice questions, a student chooses to pick an option randomly. There are four options for each questions. Answering a question correctly will give the student 1 mark, while picking a wrong option will give the student a pentalty of - 0.25 marks. There is only one correct answer for each question. What is the probability that a student will get negative marks if they follow such a strategy?
I'm stumped at even trying to model this problem. I do observe a few things, but I can't make any substantial arguments from them:
- We could have a random variable, X represent the marks a student gets while answering the 100 questions that way.
- The range of values this variable can take is from -25 (all questions wrong) and 100 (all correct).
- The expected value of this random variable is 6.25
- How do I find the variance?
- If we find the variance can we assume a normal distribution and see the area in the lower tail, below 0?