USMLE purpose: Use standard deviation rules and distinguish cohort from case-control designs.

How to use this page

  1. For normal distributions, sketch the bell curve.
  2. Memorize 68–95–99.7.
  3. For study design, ask whether anyone had the outcome at the beginning.
  4. Use the toggles before opening the explanations.

One-liner

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.

Normal distribution rule

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

Study design recognition

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

Anki-style rapid recall

Practice Questions

Question 1

A reference range is 0.08–0.12 and represents 95% around a mean of 0.10. What is the 99.7% range?