Final answer:
The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes when the waiting time is uniformly distributed between 0 and 9 minutes is 0.750, or 75%.
Step-by-step explanation:
The question asks about the probability that a passenger on a subway has a waiting time greater than 2.25 minutes when the waiting times are uniformly distributed between 0 and 9 minutes. To find this probability, we consider the properties of a uniform distribution: each period within the range is equally likely.
Since the total range is 9 minutes, and we are interested in the time after the first 2.25 minutes, we subtract 2.25 from 9 to find the remaining time period, which is 6.75 minutes. The probability is then the length of the event interval (6.75 minutes) divided by the length of the total interval (9 minutes). So, the probability is 6.75/9, which simplifies to 0.75 or 75%.
To express this value with the requested three decimal places, we get 0.750.