Empirical rule — Algebra II, what it means and where it is taught
About 68%, 95% and 99.7% lie within one, two and three deviations.
Taught in Algebra II.
Where it is taught
Practise this idea
10 questions in the course bank use Empirical rule, in The Normal Distribution. The first 8 are below; the rest are in those units.
Problem 1
Using the empirical rule, approximately: what percent of a normal population lies within one standard deviation of the mean?
Worked answer
68
About 68%
Problem 2
Using the empirical rule, approximately: what percent lies within two standard deviations?
Worked answer
95
About 95%
Problem 3
Using the empirical rule, approximately: what percent lies within three standard deviations?
Worked answer
99.7
About 99.7%
Problem 4
Using the empirical rule, approximately: heights are normal, mean 170 cm, deviation 8 cm. What percent lie between 162 and 178?
Worked answer
68
One deviation either side
About 68%
Problem 5
Using the empirical rule, approximately: same heights. What percent lie between 154 and 186?
Worked answer
95
Two deviations either side
Problem 6
Using the empirical rule, approximately: same heights. What percent are taller than 186 cm?
Worked answer
2.5
5% lies outside two deviations
Half of it is above
Problem 7
Using the empirical rule, approximately: same heights. What percent are shorter than 162 cm?
Worked answer
16
32% lies outside one deviation
Half of it is below
Problem 8
Using the empirical rule, approximately: mean 500, deviation 100. What score is at the 84th percentile?
Worked answer
600
That is one deviation above
500+100=600