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?
pbinom(19, 100, .25)
returns 0.09953041. What do you get using normal approx.? On this site it is permitted to answer your own question. $\endgroup$