COMLEX & USMLE Percentage

So, you took the COMLEX or USMLE and got some wacky three-digit score along with a two-digit score. Here's how to convert your score into an actual percentage. The statistical concept to use here is the cumulative distribution function (CDF) for a normal distribution (assuming a normal distribution). It's worth noting that the two-digit score is not a percentile score on both the COMLEX and USMLE.

The score report form will give you your three-digit score (x), a mean (mu), and standard deviation (sigma). The easy way to get your percentile is to find an online calculator and determine your "probability", meaning the probability that a score would be below yours.

This can be done using Wolfram Alpha
Example Formula: normal distribution percentile, mean=500, sd=100, x=500
Change these values at the top of the page for your test score (x) and standard deviation (sd)
Wolfram Alpha - CDF Calculator
Percentile = left-tailed p-value

Here is an example:
COMLEX three-digit score 697, mean of 500, standard deviation 121. The probability is 0.94824807, meaning there is a 95% chance that any score would be below 697. So, 697 is approximately 95th percentile.

Some other calculator options:
CDF Calculator - Star Trek Site
CDF Calculator - Daniel Soper Site

The last option would be using a Z-table...but why do the extra work?