USMLE purpose: Solve bell-curve count questions by converting standard deviations into percentages and then into patient counts.

How to use this page

  1. Identify the mean and SD.
  2. Locate the cutoff relative to the mean.
  3. Convert the region under the curve into a percent.
  4. Multiply by the sample size.

One-liner

If the cutoff is 1 SD above the mean, then everything below it is 50% + 34% = 84%.

Bell curve shortcut

Region Percent Use
Mean to +1 SD 34% Half of 68%
Below +1 SD 84% 50% below mean + 34%
Above +1 SD 16% Remaining tail
Above +2 SD 2.5% Tail beyond 95%

Worked example

Mean = 82 kg, SD = 4 kg, sample size = 1000.

Anki-style rapid recall