Probability deals with calculating the likelihood of a given event’s occurrence.

Use:

- If you are using a Standard Normal Table to determine the probability of a given Z value will yield some probability from 0 to 1 of a particular data point being either above, or below a certain point. For example, if hospital stays for admitted patients at a certain hospital are measured in hours and were found to be normally distributed with some average hours and some standard deviation; maybe the team would want to find out how many stays can be expected to last over so many hours. Or, it could be expectations for being less than so many hours.
- You would be using probability if you are using a Weibull analysis to determine the probability of something lasting so many years, or so many miles.
- Probability theory is used with binomial data where the team might be trying to find the probability of a specific number of ‘successes’.

Examples:

- Finding the probability of obtaining exactly so many successes.
- The probability of obtaining at least so many successes, or not more than so many successes.
- The Poisson distribution uses probability theory. Perhaps the team wants to find out how many defects are expected per so many linear feet of extruded plastic. The operative word is ‘per’. The Poisson distribution would result in some probability from 0 to 1 of those defects occurring. (exactly so many, more than so many, less than so many)
- The chi-square test employs the use of probability theory. The probability of a Type I error (alpha risk) is some number between -1 and +1. (Or it could be beta risk relating to a Type II error)
- The Student t-test and the F-test both use probability theories similar to that of the chi-square testing mentioned above.
- Frequency distributions, histograms, and control charts use probability theory. If you remember the 68%, 95%, and 99.73% probabilities for looking at process capability at one standard deviation, two standard deviations, or three standard deviations respectively.