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a. A test consists of 20 multiple choice questions, each with 5 alternatives for the answer. A student has not studied for the test, so she chooses the answers at random. Let X be the discrete random variable that describes the number of correct answers.
i. Determine the expected number of correct questions answered.
ii. Determine the standard deviation of the correct number of questions answered, correct to 4 decimal places.

b. A binomial random variable, Z, has a mean of 8.4 and a variance of 3.696.
i. Determine the probability of success, p.
ii. Determine the number of trials, n.

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