On this page, we'll focus on finding the values that offset the top X% of a normal distribution, for example the top 10% or top 20%. The first example below uses the standard normal distribution. The second exam uses a normal distribution with a mean of 85 and standard deviation of 5.
Minitab® – z Score Separating the Top X%
Question: What z score separates the top 10% of the z distribution from the bottom 90%?
- From the tool bar select Graph > Probability Distribution Plot > One Curve > View Probability
- Check that the Mean is 0 and the Standard deviation is 1
- Select Options
- Select A specified probability
- Select Right tail
- For Probability enter 0.10
- Click Ok
- Click Ok
This should result in the following output:
A z score of 1.282 separates the top 10% of the z distribution from the bottom 90%.
Minitab® – Value Separating the Top X%
Question: Scores on a test are normally distributed with a mean of 85 points and standard deviation of 5 points. What score separates the top 10% from the bottom 90%?
- From the tool bar select Graph > Probability Distribution Plot > One Curve > View Probability
- Change the Mean to 85 and the Standard deviation to 5
- Select Options
- Select A specified probability
- Select Right tail
- For Probability enter 0.10
- Click Ok
- Click Ok
This should result in the following output:
The test score that separates the top 10% from the bottom 90% is 91.41 points. This could also be described as the 90th percentile.