On a true/false quiz, a student who hasn\'t studied and guesses on each question

Question

On a true/false quiz, a student who hasn't studied and guesses on each question has a 50% chance of getting each question correct. On a quiz with 10 such questions, let X the number of questions the student gets correct. a. What kind of distribution does X have (give name and parameter value(s)? b. What is the expected number of questions the student will get correct? What is the standard deviation of X? c. What is the probability the students will get at least 8 of the questions correct? d. What is the probability of the student getting more than 8 questions wrong? 8.

Explanation / Answer

Solution:-

a) binomial distribution does X have p = 0.50 , n = 10

b) Expected number = n*p = 10*0.5 = 5

standard deviation = sqrt(n*p*q) = sqrt(10*0.5*0.5) = 1.5811

c. P(X > 8) = 0.0547

d. P(X < 8) = 0.9893

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