Question

On a multiple choice test with 24 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

Answer 1

The variance for the number of correct answers is 4.5.

Explanation:

For each question, there are only two possible outcomes. Either the correct answer is guessed, or it is not. Questions are independent of each other, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The variance of the binomial distribution is:

`V(X) = np(1-p)`

24 questions

This means that
`n = 24`

Each question has four possible answers one of which is correct

This means that
`p = (1)/(4) = 0.25`

Find the variance for the number of correct answers

`V(X) = np(1-p) = 24*0.25*0.75 = 4.5`

The variance for the number of correct answers is 4.5.