# A test consists of 910 true or false questions. If the student guesses on each question, what is the expected standard deviation of the number of correct answers?

$\sqrt{910 \cdot 0.5 \cdot 0.5} = \sqrt{227.5} \approx 15.08$.
The number $X$ of correct guesses in $n = 910$ trials is a binomial random variable with probability $p = 0.5$ of success. The standard deviation of such a variable is $\sqrt{n p \left(1 - p\right)}$. In this case, that's $\sqrt{910 \cdot 0.5 \cdot 0.5} = \sqrt{227.5} \approx 15.08$.
Such a variable would be well-modeled by a Normal distribution with mean $n p = 910 \cdot 0.5 = 455$ and standard devation sqrt{227.5 approx 15. Using the 68-95-99.7 rule-of-thumb , about 68% of the people who guessed on such an 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.