Final answer:
The question involves understanding the uniform distribution of waiting times for the Sky Train. It arrives every eight minutes, and the likelihood of any specific wait time within that period is the same.
Step-by-step explanation:
The question refers to the waiting times for the Sky Train, which are said to follow a uniform distribution. This means that the time between any two arrivals of the train is equally likely to be any value between 0 and 8 minutes. For example, the probability that the wait time is between 0 and 2 minutes is the same as the probability that it is between 6 and 8 minutes.
To calculate the probability of waiting for a certain amount of time, we'd use the formula for uniform distribution probability: P(a < X < b) = (b-a) / (M-m), where 'X' is the random variable representing wait time, 'a' and 'b' are the values between which we're calculating the probability, and 'M' and 'm' are the maximum and minimum values of the range, respectively.
In this scenario, since the train arrives every eight minutes and the distribution of wait times is uniform, the minimum value 'm' is 0 and the maximum value 'M' is 8. Thus, if we wanted to know the probability of waiting less than 5 minutes, we would calculate P(0 < X < 5) = (5-0) / (8-0) = 5/8.