Question

On a multiple choice test with 15 ​questions, each question has four possible​ answers, one of which is correct. For students who guess at all​ answers, find the variance for the number of correct answers. Round to the nearest tenth.

Answer 1

The variance for the number of correct answers is 2.8 questions

Explanation:

The number of correct answers follows binomial distribution, in which we have:

• n identical and independents events: the 15 questions
• two possibles results that we call success and fail: The answer is correct and the answer is incorrect
• probability p of success and 1-p of fail. Probability 1/4 of get the answer correct and probability of 3/4 of get the answer incorrect. This probabilities are calculated on that way because every question have 4 possible answers and one of which is correct.

So, the variance for a variable x that follows a Binomial distributions is:

V(x)=n*p*(1-p)

Then, the variance for the number of correct answers is:

V(x)=15*(1/4)*(3/4) = 2.8125 ≈ 2.8

Because n is equal to 15, p is equal to 1/4 and (1-p) is equal to 3/4.