According to the binomial distribution, there are 13 questions should the student expect to answer correctly.
Binomial distribution:
in statistics, binomial distribution refers the probability of getting a success must remain the same for the trials we are investigating.
Given,
A quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions.
Here we need to find how many questions should the student expect to answer correctly.
While we looking into the given question, we have identified that the total number of questions is 24.
Number of options = 4
So, the probability of getting correct answer = 1/4 = 0.25
The probability of getting incorrect answer is,
=> 1 - 1/4 = 3/4 = 0.75
So, based on the binomial distribution,
X ~ Binomial Distribution (m=25, p=0.25, q=0.75)
Then in probability it can be written as,
=> P (X=13) = (25C13)x ((0.25)¹³) x ((0.75)¹²)
=> P (X=13) = 0.00245461663
Therefore, the number of correct answers is 13.
To know more about Binomial distribution here.
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