Majari Magazine

Probability Distribution Plots

by Michael Hutagalung on 23/03/08 at 7:20 pm | 2 Comments | Print article | Email article

When scientists use the Hubble Space Telescope to explore the galaxy, they receive a stream of digitized images in the form of an endless, binary soup—incredibly valuable information that’s virtually trapped in a sea of one’s and zero’s. These numbers must be converted into pictures before the scientists can learn anything from them.

The same is true of statistical distributions and parameters used to describe sample data. They offer important information, but the numbers can be meaningless without an illustration to help you interpret them. For instance, what does it mean if your data follow a gamma distribution with a scale of 8 and a shape of 7? If the distribution shifted to a shape of 10, would that be a good thing or a bad thing? And how would you explain all of this to an audience more interested in outcomes than in learning statistics?

Minitab’s probability distribution plots create the pictures that bring the numbers to life. Even novice users can reap the benefits that come from understanding their data’s distribution. Here are a few examples.

A building materials manufacturer: See what you’ve been missing

A building materials manufacturer develops a new process to increase the strength of its I-beams. The output shows that the old process fit a gamma distribution with a scale of 8 and a shape of 7 whereas the new process has a shape of 10. The manufacturer does not know what this change in the shape parameter means.

Minitab’s probability distribution plots show that the subtle shape change increases the number of acceptable beams from 91.4% to 99.5%, an improvement of 8.1%. Additionally, the right tail appears to be much thicker indicating many more unusually strong units. Perhaps these could spawn a premium line of products.

A specialist at a grocery store: Communicate your results

A quality improvement specialist at a grocery store chain wants to implement a new but expensive program to reduce discrepancies between the item’s shelf price and the amount charged at the register. No difference is ideal but any difference within the range of ± 0.5% is considered acceptable. In the pilot study, the mean improvement is tiny and the president doesn’t see the benefits of the smaller standard deviation. Therefore, the president is reluctant to approve the costly program. The specialist knows that the tighter distribution is key to the program’s success. To illustrate this, she creates this plot to show that the differences are clustered much closer to zero and most are in the acceptable range. Now the president can see the improvement.

Fabrication department of a farm equipment manufacturer: Compare distributions

The fabrication department of a farm equipment manufacturer counts the number of tractor chassis completed per hour. A Poisson distribution with a mean of 3.2 best describes the sample data. However, the test lab would like to use an analysis that requires a normal distribution and wants to know if it is appropriate. If the normal distribution does not approximate the Poisson distribution, then the test results will be invalid. The distribution plot can easily compare the known distribution with a normal distribution. In this case, it’s clear that the normal distribution, as well as the analyses that require it, won’t be a good fit.

How to create probability distribution plots in Minitab

It’s easy to create a probability distribution plot to visualize and compare distributions, and even scrutinize an area of interest. For instance, an analyst is interested in interviewing customers with customer satisfaction scores between 115 and 135. Minitab’s Individual Distribution Identification feature shows that these scores are normally distributed with a mean of 100 and a standard deviation of 15. However, the analyst can’t visualize where his subjects fall within the range of scores, or their proportion of the entire distribution.

1. Choose Graph > Probability Distribution Plot > View Probability. Click OK.
2. From Distribution, choose Normal.
3. In Mean, type 100.
4. In Standard deviation, type 15.
5. Click the Shaded Area tab.
6. In Define Shaded Area By, choose X Value.
7. Click Middle.
8. In X value 1, type 115.
9. In X value 2, type 135.
10. Click OK.

The scores in the region of interest (115-135) represent 14.9% of the population. This somewhat small percentage suggests that the analyst may have to place extra effort in finding a sufficient number of qualified subjects.

Putting probability distribution plots to use

Probability distribution plots provide valuable insight by revealing the deeper meaning of your distributions. Use these graphs to highlight the effect of changing distributions and parameter values, show you where target values fall in a distribution, and view the proportions associated with shaded areas. These simple plots also clearly and easily communicate these advanced concepts to a non-statistical audience.

Don’t get bogged down in hard-to-understand concepts and numbers. Instead, simply use Minitab to visualize what your data are trying to tell you.

This is part of a series of articles entitled Accessing the Power of Minitab. Visit to learn more.