A multiple choice test consists of 100 questions. Each question has 5 possible answers, only one of which is correct. Four points are awarded for each correct answer, and 1 point is taken off for each wrong answer. Suppose you answer all the questions by guessing at random, independently of all other questions.
What is the chance that you get more than 30 points?

Question

A multiple choice test consists of 100 questions. Each question has 5 possible answers, only one of which is correct. Four points are awarded for each correct answer, and 1 point is taken off for each wrong answer. Suppose you answer all the questions by guessing at random, independently of all other questions.
What is the chance that you get more than 30 points?

kenljw · Answer

P(C) = .2. P(E) = .8
4P(C) - P(E) = 0
This indicates you should get mean 50 points.
As for distribution you should us binomial distribution.