SOLUTION: Because they are so easy to correct, multiple-choice questions are commonly used for class tests, SAT tests, MCAT tests for medical schools, and many other circumstances. Describe

Question 822714: Because they are so easy to correct, multiple-choice questions are commonly used for class tests, SAT tests, MCAT tests for medical schools, and many other circumstances. Describe the probability distribution for the number of correct responses when someone makes random guesses for 10 multiple-choice questions on an SAT test. Each question has 5 possible answers (a-e), one of which is correct.
Assume that random guesses are made for each of the 10 questions.
A. Find the mean number of correct responses.
B. Find the standard deviation for the numbers of correct responses when random guesses are made for the 10 questions by many different subjects.
C. What is the probability that someone gets at least half of the questions correct?
D. When someone makes guesses for all 10 answers, what is the expected number of correct answer? (use Min and Max to justify)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Describe the probability distribution for the number of correct responses when someone makes random guesses for 10 multiple-choice questions on an SAT test. Each question has 5 possible answers (a-e), one of which is correct.
Assume that random guesses are made for each of the 10 questions.
A. Find the mean number of correct responses.
u = np = 10*(1/5) = 2
--------
B. Find the standard deviation for the numbers of correct responses when random guesses are made for the 10 questions by many different subjects.
std = sqrt(npq) = sqrt(2*4/5) = 1.2649
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C. What is the probability that someone gets at least half of the questions correct?
P(10<= x <=20) = 1-P(x < 9) = 0.0026
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D. When someone makes guesses for all 10 answers, what is the expected number of correct answer?
E(x) = np = 2
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Cheers,
Stan H.
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