Analytical Probability Distributions with Excel

Abstract

This note introduces four common underlying processes and the analytical probability distribution used to forecast the outcomes of each. The note also illustrates how to use Excel functions to calculate probabilities from the four resulting probability distributions: the binomial, normal, Poisson, and exponential.

Excerpt

UVA-QA-0679

Rev. Oct. 29, 2013

ANALYTICAL PROBABILITY DISTRIBUTIONS WITH EXCEL

As a U.S. manufacturer of components for consumer electronic products in this highly competitive era, you are very concerned about product quality. You know that, on average, 5% of the components produced by one particular machine are defective, and you are wondering whether you need to replace the machine. To help answer this question, you want to know the probability of a defect-free production run of 10 components.

One way you might approach this problem is to use your judgment to make a subjective assessment of the probability distribution of the number of defects in a production run of 10 components. Unless you have a great deal of experience with similarly sized production runs, however, you may not feel particularly comfortable with the results.

An alternative approach is to reflect on the underlying process by which the number of defects will be determined. When the underlying process that generates the uncertain quantity is well understood, the probability distribution can often be determined from basic principles.

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Keywords: Probability analysis