Question

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is more than 140 minutes

Answer 1

The probabilities that a flight is more than 140 minutes would be 32.2%.

Explanation:

Given that a trip between New York and Chicago lasts between 120 and 150 minutes, with probabilities uniformly distributed within that time range, to calculate the probabilities that the trip lasts more than 140 minutes, we must perform the following calculation:

First, determine the range of minutes available for arrival. Thus, between 120 and 150, including both ends, there is a 31 minute difference (150-119). Therefore, since the 100% arrival probability is evenly distributed between these minutes, each minute has a 3.22% probability that the plane will arrive at that time (100/31 = 3.22).

Therefore, since the question points to a journey of more than 140 minutes, we must consider the time from the 141 minute journey, that is, 10 minutes between 141 and 150. Thus, the probabilities that the trip lasting more than 140 minutes will be 32.2%.