USMLE purpose: Use standard deviation rules and distinguish cohort from case-control designs.
Normal distribution questions usually test 68–95–99.7, while study-design questions usually test whether you can separate cohort → relative risk from case-control → odds ratio.
| Range | Percent included | Shortcut |
|---|---|---|
| Mean ± 1 SD | 68% | 34% on each side of mean |
| Mean ± 2 SD | 95% | 2.5% in each tail |
| Mean ± 3 SD | 99.7% | 0.15% in each tail |
| Design | Starts with | Direction | Measure |
|---|---|---|---|
| Case-control | Disease vs no disease | Looks backward for exposure | Odds ratio |
| Cohort | Exposure vs no exposure | Follows forward for outcome | Relative risk |
| Cross-sectional | One point in time | Snapshot | Prevalence |
A reference range is 0.08–0.12 and represents 95% around a mean of 0.10. What is the 99.7% range?