7.3.1 - Top X%

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 18

Minitab®  – z Score Separating the Top X%

Question: What z score separates the top 10% of the z distribution from the bottom 90%?

Steps
  1. From the tool bar select Graph > Probability Distribution Plot > One Curve > View Probability
  2. Check that the Mean is 0 and the Standard deviation is 1
  3. Select Options
  4. Select A specified probability
  5. Select Right tail
  6. For Probability enter 0.10
  7. Click Ok
  8. Click Ok

This should result in the following output:

Standard normal distribution constructed with Minitab showing the top 10%

A z score of 1.282 separates the top 10% of the z distribution from the bottom 90%.

 

Video Walkthrough

Minitab 18

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%?

Steps
  1. From the tool bar select Graph > Probability Distribution Plot > One Curve > View Probability
  2. Change the Mean to 85 and the Standard deviation to 5
  3. Select Options
  4. Select A specified probability
  5. Select Right tail
  6. For Probability enter 0.10
  7. Click Ok
  8. Click Ok

This should result in the following output:

Normal distribution constructed in Minitab with a mean of 85 and standard deviation of 5 showing the top 10%

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.

 

Video Walkthrough