68-95-99.7 Rule Interactive Learning
The 68-95-99.7 Rule
The 68-95-99.7 rule (also called the Empirical Rule) describes how data is distributed in a normal distribution:
- 68% of data falls within 1 standard deviation (σ) of the mean (μ)
- 95% of data falls within 2σ of the mean
- 99.7% of data falls within 3σ of the mean
Interactive Normal Distribution
Detailed Distribution Breakdown
Click on any colored section to see its exact percentage
Practice Question 1
If test scores are normally distributed with a mean of 80 and standard deviation of 5:
What percentage of students scored between 75 and 85?
This range is from μ-σ (80-5=75) to μ+σ (80+5=85), so it covers 68% of students.
Practice Question 2
Heights of adult men are normally distributed with mean 70 inches and σ=3 inches:
What percentage of men are between 64 and 76 inches tall?
64 is μ-2σ (70-6=64) and 76 is μ+2σ (70+6=76), so this covers 95% of men.
Practice Question 3
IQ scores have μ=100 and σ=15:
Between what two scores would you expect to find 99.7% of people?
99.7% covers μ±3σ, so from 100-45=55 to 100+45=145. 55 to 145.
Normal Distribution Calculator
Common Z-Score Values
| Z-Score | Area to Left | Area to Right | Between ±Z |
|---|---|---|---|
| 0.0 | 50.00% | 50.00% | 0.00% |
| 0.5 | 69.15% | 30.85% | 38.30% |
| 1.0 | 84.13% | 15.87% | 68.27% |
| 1.5 | 93.32% | 6.68% | 86.64% |
| 2.0 | 97.72% | 2.28% | 95.45% |
| 2.5 | 99.38% | 0.62% | 98.76% |
| 3.0 | 99.87% | 0.13% | 99.73% |