You take a 20-question multiple choice exam on which every correct answer is worth 1 point, and every incorrect answer is worth − 1 4 points to discourage guessing. Each question has five options: (A) through (E). On each question, you are able to eliminate one of the options as certainly wrong (leaving four), and then guess randomly between the other four options. (a) The number of correct answers you give is a random variable X with a binomial distribution. What are the parameters (n and p) of that distribution? (b) Express the number of points you receive as a linear transformation aX + b of X, the random variable from part (a). (c) Find the probability that you get exactly 12.5 points.
2. You take a 20-question multiple choice exam on which every correct answer is worth 1 point, and every incorrect answer is worth − 1 4 points to discourage guessing. Each question has five options: (A) through (E). On each question, you are able to eliminate one of the options as certainly wrong (leaving four), and then guess randomly between the other four options.
(a) The number of correct answers you give is a random variable X with a binomial distribution. What are the parameters (n and p) of that distribution?
(b) Express the number of points you receive as a linear transformation aX + b of X, the random variable from part (a).
(c) Find the probability that you get exactly 12.5 points.
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