An exam has 5 questions and each of them has 4 possible answers. a student gets 3 points for each correct answer and loses 1 point for each wrong answer. consider a student who answers all questions completely at random. let x denote the number of correct answers and y the number of points of this student at the end of the test. (a negative score is possible). (a) compute the mean and the standard deviation of y , µy and σy . (b) compute p(µy − σy ≤ y ≤ µy + σy ) and p(µy − 2σy ≤ y ≤ µy + 2σy ). (c) what is the probability that the student above gets a positive score?