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PreMBA Analytical Methods
Continuous Probability Distributions: Introduction

A variable is continuous if the range of possible values for that variable falls along a continuum. You probably recall from the Discrete Probability Distributions section of this course that discrete random variables are measured in whole units, such as the number of people attending a ball game, the number of cookies in a package, or the number of cars assembled during one production shift. Continuous random variables are measured along a continuum, such as the loudness of cheering at a ball game, the weight of cookies in a package, or the time required to assemble a car.

A continuous probability distribution illustrates the complete range of values a continuous random variable can take on, as well as the probabilities associated with that range of values. A continuous probability distribution is important in predicting the likelihood of an event within a certain range of values.

As an example, consider temperature. Temperature is a continuous random variable because its possible values fall along a continuum. Automobile manufacturers want to be sure that the cold temperatures of northern climates do not cause fractures in vehicle parts. In this example, the temperature at which such fractures occur is a continuous random variable. For these manufacturers, determining the exact temperature at which vehicle parts develop fractures is impossible, as there are an infinite number of fractions of degree between, for example, –30 degrees and –35 degrees.

Although the specific temperature fracture point is impossible to discover, automobile manufacturers can determine the probability that fractures will occur within the range of temperatures experienced during a typical northern winter. The manufacturers would use a continuous probability distribution to determine the probability of fractures at or below a given temperature.

When you have completed the Continuous Probability Distributions section, you should be able to

  • interpret a continuous probability distribution
  • identify a normal distribution and explain the significance of a normal distribution's mean and standard deviation
  • calculate a random variable's Z score and determine probabilities based on that Z score
  • use a Z distribution table

When does a supply chain manager use continuous probability?

Low bandwith

High bandwith
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