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A quiz consists of 60 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?

User SwapsCAPS
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Answer: √910 . 0.5 . 0.5= √227.5≈ 15.08.

Explanation: The number x of correct guesses in n=910

trials is a binomial random variable with probably p= 0.5 of success. The standard deviation of such a variable is √np(1 -- p ). In this case, that's √910 . 0.5 . 0.5=√227.5≈ 15.08.

Such a variable would be well modeled by a normal distribution with mean np= 910 . 0.5= 455 and standard deviation √222.75 ≈ 15. using the 68-95.99.7 rule-of-thumb , about 68% of the people who guessed on such a exam would score between 440 and 470, about 95% of such people would score between 425 and 485, and about 99.7% of such people would score between 410 and 500

User Antonino Bonumore
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