Answer:
The mean for the number of correct answers is 5.5
Step-by-step 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:
[tex]E(X) = np[/tex]
22 questions
This means that [tex]n = 22[/tex]
Each question has four possible answers, one of which is correct.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
For students who guess at all answers, find the mean for the number of correct answers.
[tex]E(X) = np = 22*0.25 = 5.5[/tex]
The mean for the number of correct answers is 5.5
