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:

z distribution constructed with Minitab showing the bottom 10%

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:

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

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

Video Walkthrough


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