DECISION THEORY AND THE NORMAL DISTRIBUTION
After completing this module, students will be able to: 1. Understand how the normal curve can be used in performing break-even analysis. 2. Compute the expected value of perfect information using the normal curve. 3. Perform marginal analysis where products have a constant marginal profit and loss.
M3.1 M3.2 M3.3
Introduction Break-Even Analysis and the Normal Distribution Expected Value of Perfect Information and the Normal Distribution
Summary • Glossary • Key Equations • Solved Problems • Self-Test • Discussion Questions and Problems • Bibliography
Appendix M3.1: Derivation of the Break-Even Point Appendix M3.2: Unit Normal Loss …ver más…
But actual demand is not known. Rudy decides to turn to the use of a probability distribution to estimate demand.
Probability Distribution of Demand
Actual demand for the new game can be at any level—0 units, 1 unit, 2 units, 3 units, up to many thousands of units. Rudy needs to establish the probability of various levels of demand in order to proceed. In many business situations the normal probability distribution is used to estimate the demand for a new product. It is appropriate when sales are symmetric around the mean expected demand and follow a bell-shaped distribution. Figure M3.1 illustrates a typical normal curve that we discussed at length in Chapter 2. Each curve has a unique shape that depends on two factors: the mean of the distribution (µ) and the standard deviation of the distribution (σ). For Rudy Barclay to use the normal distribution in decision making, he must be able to specify values for µ and σ. This isn’t always easy for a manager to do directly, but if he or she has some idea of the spread, an analyst can determine the appropriate values. In the Barclay example, Rudy might think that the most likely sales figure is 8,000 but that demand might go as low as 5,000 or as high as 11,000. Sales could conceivably go even beyond those limits; say, there is a 15% chance of being below 5,000 and another 15% chance of being above 11,000.
The normal distribution can be used to estimate demand.