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Introductory Business Statistics 2e

5.2 The Uniform Distribution

Introductory Business Statistics 2e5.2 The Uniform Distribution

The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints.

The mathematical statement of the uniform distribution is

f(x) = 1 ba 1 ba for axb

where a = the lowest value of x and b = the highest value of x.

Formulas for the theoretical mean and standard deviation are

μ= a+b 2 μ= a+b 2 and σ= (ba) 2 12 σ= (ba) 2 12

Example 5.2

The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive.


a. What is the probability that a person waits fewer than 12.5 minutes?


b. On the average, how long must a person wait? Find the mean, μ, and the standard deviation, σ.


c. Ninety percent of the time, the time a person must wait falls below what value?


This asks for the 90th percentile.

Try It 5.2

The total duration of baseball games in the major league in a typical season is uniformly distributed between 447 hours and 521 hours inclusive.

  1. Find a and b and describe what they represent.
  2. Write the distribution.
  3. Find the mean and the standard deviation.
  4. What is the probability that the duration of games for a team in a single season is between 480 and 500 hours?

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