Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time 2.25 minutes.

Answer 1

Using the uniform distribution, it is found that there is a 0.625 = 62.5% probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

An uniform distribution has two bounds, a and b.

The probability of finding a value above x is:

In this problem, uniformly distributed between 0 and 6 minutes, thus .

The probability of a time greater than 2.25 minutes is P(X > 2.25), thus:

0.625 = 62.5% probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.