An exam has 5 questions and each of them has 4possible 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 numberof correct answers and
Y the number of points of this student at the end of the test. (Anegative 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 positivescore?
