SOLUTION: A test consists of 10 true/false questions. To pass the test a student must answer at least 8 questions correctly. a. If a student guesses on each question, what is the probabilit

Question 1083819: A test consists of 10 true/false questions. To pass the test a student must answer at least 8 questions correctly.
a. If a student guesses on each question, what is the probability that the student will pass
the test?
b. Find the mean and standard deviation of the number of correct answers.
c. Is it unusual for a student to pass by guessing? Explain.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
this is an application of the binomial probability distribution
:
in a true/false test, you have a 50% chance of guessing correctly
:
a) Probability(P) (8 correct choices out of 10 trials) = 10C8 * (0.50)^8 * (1-0.50)^(10-8) = 0.04
:
Note 10C8 = 10! / (8! * (10-8)!)
:
b) mean = 10 * 0.50 = 5, standard deviation = square root(10 * 0.50 * (1-0.50)) = 1.58
:
c) yes, from b the student can not achieve passing grade by guessing. If the test has 5 true and 5 false correct answers, best the student can do is 5. If there is an unequal amount of true and false correct answers, the spread is (3.42 to 6.58)
:

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