SOLUTION: The GRE is an entrance exam that most students are required to take upon entering graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approx

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Question 970146: The GRE is an entrance exam that most students are required to take upon entering graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.
What percent of scores were between 286 and 322? Round your answer to the nearest whole number
Answer by Evy Hofbauer(7) About Me  (Show Source):
You can put this solution on YOUR website!
68% of the distribution lies within one standard deviation of the mean. about 95% is within 2 stdv.
So add and subtract 12 to each side of the mean. This will get you the interval of 298 to 322.
286 + 12 = 298 so another standard deviation on the lower side of the interval is needed.
Subtract the 1 stdv from 2 stdv to find how much more of the data 2 stdvs includes.
95% - 68% = 27%
Divide 27% by 2 because we only need the left.
27% ÷2 = 13.5%
Finally add 13.5% to 1 stdv to get the total.
13.5% + 68% = 81.5% for the interval from 286 to 322.
Rounded to 82%.