# CHAPTER 7

# Business Problems That Depend on Knowing “How Much”

## 7.0. Introduction: What Is the Issue?

Some uncertain business outcomes can take a truly huge number of possible values. For instance, the demand for grain next month might be any number between 0 and 1000 tons. If you measure this to the nearest kilogram then there are a million possible outcomes—from 1 to 1,000,000kg. If you wanted the *probability distribution* of this variable you would have to list all these outcomes and the probability of each! This is hardly practical. Not to mention that if we measured the grain demand to the nearest gram rather than kilogram then there would be a billion possible outcomes!

For variables that take an effectively infinite number of values we do not use the probability function to describe their uncertain behavior. Instead we use a curve, and areas beneath the curve represent probabilities. The two most useful distributions of this kind are the **normal** and the** lognormal**. Here are some examples where you could use the methods of this chapter.

Suppose someone sits a management aptitude test and get a score of 123.1. How good is this score? What percentile would the person be in?

Suppose we are filling a bag of product with a target weight of 10kg. There is a typical 22-g uncertainty in the amount of product delivered. In order to satisfy the packing claim of 10kg, we set the fill level slightly above 10kg. How likely is it that the bag will contain at least 10kg of product?

A manufactured ...