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### Middle/High School Algebra, Geometry, and Statistics (AGS)9.30 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?30.65%65%28.65% Q 2: If athletic shoes last an average of 1.5 years, what is the probability that a randomly selected pair of athletic shoes will last less than 6 months?58.66%48.45%28.35% Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!

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