Question

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?

Answer 1

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