# 7.3.2 - Bottom X%

7.3.2 - Bottom X%

Next, we'll find the z scores or observations that off set the bottom X% of a normal distribution. Earlier in this lesson, we learned that this is also known as the cumulative proportion or percentile. The first example below uses the z distribution. The second example uses a normal distribution with a mean of 85 and standard deviation of 5.

## Minitab® – z Score Separating the Bottom X%

Question: What z score separates the bottom 10% of the standard normal distribution from the top 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 Left tail
6. For Probability enter 0.10
7. Click Ok
8. Click Ok

This should result in the following output:

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

Video Walkthrough

## Minitab® – Value on a Normal Distribution Separating the Bottom X%

Question: Scores on a test are normally distributed with a mean of 85 points and standard deviation of 5 points. What score is the 10th percentile? In other words, what score separates the bottom 10% from the top 90% of this distribution?

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 Left tail
6. For Probability enter 0.10
7. Click Ok
8. Click Ok

This should result in the following output:

The 10th percentile on this test is a score of 78.59 points.

Video Walkthrough

 [1] Link ↥ Has Tooltip/Popover Toggleable Visibility