The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

Since the waiting times are uniformly distributed between 0 and 6 minutes, the total range of times is 6 minutes. Probability in a uniform distribution is equal to the area under the curve within a certain interval, and since we're dealing with a uniform distribution, this amounts to simply the length of the interval of interest divided by the total length of time.

The probability that a randomly selected passenger waits more than 2.25 minutes can be found by considering the interval from 2.25 minutes to the maximum time of 6 minutes. The length of this interval is 6 - 2.25 = 3.75 minutes.

To find the probability, divide the length of the interval where the passenger waits longer than 2.25 minutes by the total spread of possible waiting times (which is 6 minutes):

Probability (waiting time > 2.25) = Length of interval / Total length of time P(waiting time > 2.25) = 3.75 / 6

Now, perform the calculation:

P(waiting time > 2.25) = 0.625

So, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is 0.625, or 62.5%.