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High School Mathematics - 2
11.10 Exponential Distributions

Exponential Distributions:
  • The exponential distributions are a class of continuous probability distributions.
  • They are used to predict the probabilities of events based on time.
  • They are most commonly used to measure reliability, which is the amount of time that a product lasts.
  • They apply in situations where the time spent on an event or the amount of time that an event lasts is important.
  • They are represented as following functions:
    • f(x) = e-mx gives the probability f(x) that something lasts longer or costs more than the given value x, where m is the multiplicative inverse of the mean amount of time.
    • f(x) = 1- e-mx gives the probability f(x) that something does not last as long or costs more than the given value x, where m is the multiplicative inverse of the mean amount of time.
  • Exponential distributions are represented by the curve:
  • The x-axis usually represents length of time or money. The y-axis represents probability.

Directions: Answer the following questions. Also write at least 5 examples of your own.
Q 1: At a certain store customers arrive at an average of 15 per hour. What is the probability that the manager must wait at least 5 minutes for the first customer?
65%
30.65%
28.65%

Q 2: _________ distributions are used to predict the probabilities of events based on time.
Binomial
Exponential
Normal

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!


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