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 greater than 3.25 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes. \( \square \) (Simplify your answer. Round to three decimal places as needed.)

To determine the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes, we can use the properties of uniform distribution. The waiting times are uniformly distributed between 0 and 7 minutes. This means the total possible waiting time is: \[ 7 - 0 = 7 \, \text{minutes} \] Next, we calculate the range of waiting times that are greater than 3.25 minutes. The waiting times greater than 3.25 minutes fall between 3.25 and 7 minutes. The length of this interval is: \[ 7 - 3.25 = 3.75 \, \text{minutes} \] Now, we can compute the probability: \[ P(X > 3.25) = \frac{\text{Length of the interval where } X > 3.25}{\text{Total interval length}} \] So, substituting our values, we get: \[ P(X > 3.25) = \frac{3.75}{7} \] Calculating that gives: \[ P(X > 3.25) = 0.5357 \] When rounded to three decimal places, the probability is: \[ P(X > 3.25) \approx 0.536 \] So, the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is approximately \( \boxed{0.536} \).