5.118 For each situation, state if a binomial distribution is reasonable for the

Question

5.118 For each situation, state if a binomial distribution is reasonable for the random variable X. Justify your answer. (a) A multiple-choice examination consists of 10 problems, each of which has 5 suggested answers. A student marks answers by pure guesses i.e., one answer is chosen at random out of the 5), and X denotes the number of marked answers that are wrong. (b) A multiple-choice examination has two parts: Part 1 has 8 problems, each with 5 suggested answers, and Part 2 has 10 problems, each with 4 suggested answers. A student marks answers by pure guesses, and X denotes the total number of problems that the student correctly answers. (c) Twenty-five married couples are interviewed about exercise, and X denotes the number of persons (out of the 50 people interviewed) wheo exercise regularly.

Explanation / Answer

5.118 For each situation, state if a binomial distribution is reasonable for the random variable X. Justify your answer. (a) A multiple-choice examination consists of 10 problems, each of which has 5 suggested answers. A student marks answers by pure guesses i.e., one answer is chosen at random out of the 5), and X denotes the number of marked answers that are wrong. (b) A multiple-choice examination has two parts: Part 1 has 8 problems, each with 5 suggested answers, and Part 2 has 10 problems, each with 4 suggested answers. A student marks answers by pure guesses, and X denotes the total number of problems that the student correctly answers. (c) Twenty-five married couples are interviewed about exercise, and X denotes the number of persons (out of the 50 people interviewed) wheo exercise regularly.

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