Final answer:
The probability that a passenger will wait more than 5 minutes for a shuttle train completing a circuit every 7 minutes is 2/7, or approximately 28.57%.
Step-by-step explanation:
The question asks for the probability that a passenger will wait more than 5 minutes for a shuttle train that completes its circuit every 7 minutes. We know that wait times are uniformly distributed over the interval from 0 to 7 minutes. So, if we want to find the probability of waiting more than 5 minutes, we can look at the interval from 5 to 7 minutes.
The length of this interval is 2 minutes, and since the total interval is 7 minutes, we calculate the probability by dividing the length of the interval that represents waiting more than 5 minutes by the total interval length:
Probability = (2 minutes) / (7 minutes) = 2/7
Therefore, the probability that a passenger will wait more than 5 minutes is 2/7, which is approximately 0.2857 or 28.57%.