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.
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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 there are 5 choices for each question, the probability of guessing correctly on any one question is 1/5. Therefore, we can model the number of correct answers using a binomial distribution with n=45 and p=1/5. The expected value or the mean of this distribution is np=45/5=9. The standard deviation of a binomial distribution is sqrt(np(1-p)), which in this case is sqrt(45/5 x 4/5) = sqrt(36) = 6. Therefore, the student can expect to answer 9 questions correctly on average, with a standard deviation of 6.

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