A multiple-choice test has 45 questions and 5 choices for each question. If a student is totally unprepared and guesses on each question, how many questions can she expect to answer correctly, and what is the standard deviation of the number of correct answers? Round any estimated quantities to two decimal places.
A)
B)
C)
D)
E)

Question

A multiple-choice test has 45 questions and 5 choices for each question. If a student is totally unprepared and guesses on each question, how many questions can she expect to answer correctly, and what is the standard deviation of the number of correct answers? Round any estimated quantities to two decimal places. ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

Since the student is guessing on each question, then the probability of getting each question correct is 1/5. We can model the situation as a binomial distribution with n=45 and p=1/5. The expected value is given by np = 45/5 = 9. The variance is given by np(1-p) = 45/5 * (4/5) = 36/5. The standard deviation is the square root of the variance, which is approximately 2.68. Rounded to two decimal places, the expected number of correct answers is 9 and the standard deviation is 2.68. Therefore, the best choice is B.

A Multiple-Choice Test Has 45 Questions and 5 Choices for Each