SOLUTION: The probability that a student guesses the correct answer to a four​-choice multiple choice question is ​P(correct)=0.25. How many correct answers should a student expect to gu

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Question 1191773: The probability that a student guesses the correct answer to a four​-choice multiple choice question is ​P(correct)=0.25. How many correct answers should a student expect to guess on a test with 68 four​-choice multiple choice​ questions?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

n = 68 = sample size
p = 0.25 = probability of success

mu = mean
mu = n*p
mu = 68*0.25
mu = 17

The student should expect to get 17 correct answers on average.

The actual correct number will vary because this is a random process, but notice I used the phrasing "on average".
This means that if say 10,000 students did these exams and all randomly guessed, then we'd expect the correct answer count to be somewhere close to 17.

For more information, check out the binomial distribution.

Answer: 17

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

It follows from the definition of Math expectation that


    Math expectation in this problem is  0.25*68 = 17.    ANSWER