How to Find a Percentile From a Normal Distribution

The percentiles of a distribution are the numbers which a certain proportion of subjects are higher than. For example, the 75th percentile of weight means the weight which is higher than 75 percent of people. A normal distribution is the familiar bell shaped curve. Many variables are distributed approximately normally, for example height, weight and IQ.



Scores on a normal distribution are typically given in z units. These are simply the number of standard deviations above or below the mean. For example, the mean IQ is 100 and the standard deviation is 15, so an IQ of 85 has a z score of (85 - 100)/15 = -1.

Things You'll Need

• Computer with Excel

Instructions

1. Compute the z score, if this is not already done. Subtract the score for which you want the percentile from the mean score, and divide by the standard deviation.

2. Enter the z-score in cell A1 in Excel. For example, -2.1.

3. In cell A2 enter =NORM.DIST(A1,0,1,TRUE). If you entered -2.1 in cell A1, this should be 0.017864.

4. Multiply the result by 100 and this is the percentile. Continuing the example, this would give 1.7864, meaning that a z score of -2.1 is higher than 1.7864 percent of all scores.

References

• Wolfram MathWorld
• Exel Help: NORMDIST