Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes. 

Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.

Answer 1

The pdf of uniformly distribution is given by

f(x) = 1/(b-a) for 0 < x < 9

f(x) = 1/(9-0)

Height of shaded region = f(x) = 1/9

Height of shaded region = f(x) = 0.1111

Now calculate

P(greater than 4.25) = (length of shaded region) * (Height of shaded region)

= (9 - 4.25) * 0.1111

P(greater than 4.25) = 0.5277

Probability that randomly selected passenger has waiting time grater than 4.25 minutes is 0.5277.