Final answer:
The probability that the trip from Lancaster to Chillicothe takes at most 65 minutes is 5/14, using the principles of uniform distribution.
Step-by-step explanation:
The subject of this question involves probability and the properties of the uniform distribution. To find the probability that the trip takes at most 65 minutes, we'll use the principles of the uniform distribution. Since the total time for the trip varies uniformly between 60 and 74 minutes, every minute within this range is equally likely.
To calculate the probability, we first determine the length of the interval of possible times (74 - 60 = 14 minutes) and the length of the interval of interest (65 - 60 = 5 minutes). The probability, then, is simply the length of the interval of interest divided by the length of the total interval. This is calculated as:
Probability = (Interval of interest) / (Total interval) = 5/14
Therefore, the probability that the trip takes at most 65 minutes is 5/14.