Applying the Empirical Rule in a Normal Distribution

What percentage of data in a normal distribution lies between the mean and 1 standard deviation above the mean?

34% (half of 68%).

What percentage of data falls outside of 2 standard deviations from the mean (combined across both tails)?

5% (100% - 95%).

A sample has a mean of 100 and a standard deviation of 15. Between which two values does approximately 95% of the data fall?

70 and 130 (100 - 2(15) = 70; 100 + 2(15) = 130).

Using the same distribution (mean = 100, standard deviation = 15), what percentage of values is greater than 115?

16% (50% - 34% = 16%, or 13.5% + 2.35% + 0.15%).

What percentage of values falls between 1 standard deviation below the mean and 2 standard deviations above the mean?

81.5% (34% + 34% + 13.5%).

In a group of 500 adult heights with a mean of 66 inches and standard deviation of 3 inches, approximately how many people are taller than 72 inches?

About 12 or 13 people (72 inches is 2 standard deviations above the mean; 2.5% of 500 = 12.5).