Final answer:
The probability that a person waits fewer than 12.5 minutes for a bus is 0.833.
Step-by-step explanation:
The given information states that the amount of time a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive.
To find the probability that a person waits fewer than 12.5 minutes, we need to calculate the proportion of the total interval that represents that time range.
Since the distribution is uniform, the probability is equal to the length of the interval from zero to 12.5 minutes divided by the total length of the interval from zero to 15 minutes.
Probability = (12.5 minutes - 0 minutes) / (15 minutes - 0 minutes) = 12.5 / 15 = 0.833