Which one of the following is a correct statement based on a distribution with a mean of 750 and standard deviation of 25?
A) About 2.5% of the scores in the distribution are greater than 675.
B) About 50% of the scores in the distribution are less than 725.
C) About 84% of the scores in the distribution are less than 775.
D) About 95% of the scores in the distribution are less than 700.

Question

Quizplus · Accepted Answer

Option C is correct because it uses the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. A score of 775 is one standard deviation above the mean (750 + 25), so about 84% of the scores would be less than 775 (50% below the mean plus 34% within one standard deviation above the mean).

Which One of the Following Is a Correct Statement Based