Question

On a multiple choice test with 2222 ​questions, each question has four possible​ answers, one of which is correct. For students who guess at all​ answers, find the mean for the number of correct answers. Round to the nearest tenth. g

Answer 1

The mean for the number of correct answers is 5.5

Explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not guessed correctly. The probability of a question being guessed correctly is independent of other questions. 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 expected value of the binomial distribution is:

`E(X) = np`

22 ​questions

This means that
`n = 22`

Each question has four possible​ answers, one of which is correct.

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

For students who guess at all​ answers, find the mean for the number of correct answers.

`E(X) = np = 22*0.25 = 5.5`

The mean for the number of correct answers is 5.5