Question

A subway train on the Red Line arrives every 8 minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.
Find the probability that the commuter waits between two and three minutes. (Enter your answer as a fraction.)

State "60% of commuters wait more than how long for the train?" in a probability question. (Enter your answer to one decimal place.)

Find the probability that the commuter waits more than_____minutes.

Draw the picture and find the probability. (Enter your answer to one decimal place.)

Answer 1

Let X be the length of the time a computer must wait for the train to arrive (length in minutes).

A subway train on the Red Line arrives every 8 minutes during rush hour.

So, X ~ Uniform (a = 0, b = 8)

We want to find the value of x such that, P(X > x) = 0.60

P(X > x) = ( b - x) / (b - a)

=> 0.60 = ( 8 - x) / (8 - 0)

=> 0.60 = (8 - x) / 8

=> (8 - x) = 0.60 * 8

=> 8 - x = 4.8

=> x = 8 - 4.8

=> x = 3.2

Therefore, the probability that the commuter waits more than 3.2 minutes.

Answer : 3.2 minutes