In Unit 3 we learned about discrete probability distributions: Hypergeometric, Binomial, and Poisson. In Unit 4, we added the Normal distribution to our list as the first of many continuous distributions. In this unit, we are adding those other continuous probability distributions. We are seeing that the Exponential, Gamma, Weibull, Lognormal, and Beta distributions are appropriate to certain types of engineering problems. Although our readings have tended to focus the most attention on the Normal distributions, we need to recognize that to solve a particular engineering challenge, any of these distributions might be needed. We need to be able to determine which, if any, of these distributions fits any situation in which we might be doing analysis.

We use a probability plot as a tool to determine if a set of data we are analyzing can reasonably be described by one of our probability distributions. I so, then the standard probabilities associated with the distribution can be used to make predictions about the process or system represented by our data. If not, we have to do some extra math to determine our own probabilities by fitting the data we have to an algebraic function (something we'll do when we get to linear and nonlinear regression) and then integrating that function over our range of interest to determine probabilities. The math isn't that difficult once we know the function, but it is certainly faster and easier to do our work if we can quickly show that one of the distributions we already understand fits our data well enough to use it.

Discuss how a probability plot works, and why we can draw conclusions based on the level of fit we see. If the resulting "fit" isn't perfect (which it very rarely is), what factors do you need to consider in making a decision about whether to use a particular distribution to solve your challenge? Describe how you would go about determining the best distribution for a set of data (if there actually is one).