The following activities and questions relate to material covered in Chapter 5.2 The Uniform Distribution in Introductory Business Statistics (OpenStax).

Questions

1. The White Pass & Yukon Route Railway is a well-known tourist attraction bringing people between Skagway Alaska and Carcross Yukon. The time that the train takes is a uniformly distributed random variable that lies between 2.4 hours and 2.6 hours to complete a round trip. Imagine that you are in Skagway and have just missed the first train of the day and decide to wait for the next one.^[1] What is the probability that you will wait fewer than 150 minutes?

Solutions

1. Let X = the number of minutes you must wait for the train
   a = 2.4 hours = 144 minutes
   b = 2.6 hours = 156 minutes
   P(135 < x < 155 ) = [latex]\dfrac{(150-144)}{(156-144)} = \dfrac{6}{12}[/latex] = 50%
   There is a 50% chance that you will wait fewer than 150 minutes for the next train.

Media Attributions

• Carcross by Lisa Kanary is licensed under a CC BY 4.0 licence.