The waiting times for commuters on the Red Line during peak rush hours follow a uniform distribution between 0 minutes and 12 minutes.

Question

The waiting times for commuters on the Red Line during peak rush hours follow a uniform distribution between 0 minutes and 12 minutes.

Compute the height of the uniform distribution.  Leave your answer as a fraction.

Corr

What is the probability that a randomly selected commuter on the Red Line during peak rush hours waits between 3 and 11 minutes?  Give your answer as a fraction.

     

Give your answer accurate to three decimal places.

     

What is the probability that a randomly selected commuter on the Red Line during peak rush hours waits exactly 3 minutes? 

Answer 1

This is a continuous uniform distribution between 0 and 12 minute. The probability distribution curve is a rectangle with a width of 12 (0 to 12 minutes). The area under the probability distribution curve must equal 1, and since the area of the rectangle is equal to width x height, height x 12 = 1. So the height of the probability distribution = 1/12.

The probability that a randomly selected commuter waits between 3 and 11 minutes is the area under the probability distribution between 3 and 11 minutes, a width of 8 minutes

The height of the distribution is 1/12 and area is height x width so 8 x 1/12 = 8/12 or 0.667. The probability that a randomly selected commuter waits between 3 and 11 minutes is 0.667.

There is no area under the line at exactly 3 minutes, so the probability is zero. Remember that when we work with continuous distributions, the probability of an exact X is always 0, so we get probabilities by looking at the area between to limits.