The empirical rule (also called the 68-95-99.7 rule) states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and roughly 99.7% falls within three standard deviations.
Most data clusters near the center of a bell curve; the further from the mean, the rarer the value.
Showing a random 20 of 50 problems.
Example 1
challenge
In a normal distribution, what percent of data lies between +1σ and +2σ above the mean?What percent lies between +1σ and +2σ?
Example 2
medium
Heights of adult men are normal with μ=70 in, σ=3 in. Estimate the proportion of men taller than 76 in.
Example 3
medium
Heights are normal, μ=170, σ=10. What percent of people are between 150 and 190 cm?Heights: μ
Example 4
medium
IQ scores are normal with μ=100, σ=15. What percent of people have IQ between 85 and 115?IQ: μ
Example 5
medium
A normal distribution has μ=70, σ=5. What percent of data lies above 80?μ
Example 6
easy
In a normal distribution with μ=0, σ=1, what percent lies between −3 and 3?Standard normal: what percent lies between −3 and 3?
Example 7
easy
True or false: the empirical rule applies to any distribution.
Example 8
medium
True or false: the empirical rule percentages are exact for all data sets.
Example 9
medium
A normal distribution, μ=80, σ=6. What percent of data lies below 74?μ
Example 10
easy
About what percent of normal data lies within 3 standard deviations of the mean?What percent lies within ±3σ?
Example 11
easy
Fill in: in a normal distribution, about 34% of data lies between the mean and ____.
Example 12
hard
A normal distribution has μ=0, σ=1. About what percent of values lie above 1?Standard normal: what percent lies above 1 (i.e., above μ+σ)?
Example 13
hard
Heights of women are normal with μ=64 in, σ=3 in. About how many women out of 1000 are between 58 and 70 inches tall?
Example 14
medium
A normal distribution has μ=20, σ=3. What percent of data lies between 14 and 23?
Example 15
easy
In a normal distribution, what percent of data lies OUTSIDE 2 standard deviations?What percent lies outside ±2σ?
Example 16
easy
About what percent of normal data lies within 2 standard deviations of the mean?What percent lies within ±2σ?
Example 17
medium
SAT scores are normal with μ=1000, σ=200. What percent of test-takers score between 800 and 1200?SAT: μ
Example 18
medium
A normal distribution, μ=100, σ=10. What percent lies between 90 and 120?μ
Example 19
challenge
A factory's part lengths are normal with μ=50 mm, σ=2 mm. Parts outside 46 to 54 mm are scrapped. What percent is scrapped?μ
Example 20
medium
SAT scores are normal with μ=1000, σ=200. What percent score above 1400?SAT: μ