Question

A quiz consists of 20 multiple choice​ questions, each with five possible​ answers, only one of which is correct. If a student guesses on each​ question, what is the mean and standard deviation of the number of correct​ answers? Round to the nearest thousandth.

______________________________________________________________

A. The mean is 10. The standard deviation is 3.162.

B.The mean is 4. The standard deviation is 1.789.

C.The mean is 10. The standard deviation is 1.789.

D.The mean is 4. The standard deviation is 2.

Answer 1

The correct option is B.The mean is 4. The standard deviation is 1.789 [ANSWER]

Explanation:

We are given that on each question there are five possible answers out of which only one is correct. Thus, if a student guesses on a question the probability that s/he will answer it correctly is given by:

P(correctly answering a question) = (Number of correct answers) / (Total number of possible answers) = 1/5

Now, let X denote number of questions guessed correctly by a student (out of the 20 questions on the quiz) if s/he guesses on each question. Since, there is a fixed number of questions (equal to 20), each question has two possible outcomes (correctly answered or not correctly answered) and each question is correctly answered with probability 1/5 independent of other questions, thus we can conclude that:
X ~ Binomial(n = 20, p = 1/5)

Thus, the mean and standard deviation of the number of correct answers is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.