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.

The variance for the number of correct answers is 2.8 questions

Step-by-step 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.