Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

# 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 * 0.5 * 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{np(1-p)}. In this case, that's sqrt{910 * 0.5 * 0.5}=sqrt{227.5} approx 15.08.

Such a variable would be well-modeled by a Normal distribution with mean np=910 * 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.

These are approximations and we are not making a distinction between these ranges including the endpoints or not. The "half-unit (continuity) correction " could be used along with a table of Normal probabilities to try to make these estimates more precise.