Final answer:
The probabilities that the flight will be no more than 5 minutes late and more than 10 minutes late are 0.50 and 0.25, respectively. The expected flight time is 130 minutes.
Step-by-step explanation:
The student's question relates to the probability of a flight's arrival time being uniformly distributed between 120 and 140 minutes. The calculations required involve uniform distributions, which are a part of probability theory within mathematics.
A. The probability that the flight will be no more than 5 minutes late can be found using the properties of a uniform distribution. Since Delta Airlines quotes a flight time of 125 minutes, a flight time of up to 130 minutes (125 + 5) is considered no more than 5 minutes late. The length of the interval for being on time or up to 5 minutes late is 130 - 120 = 10 minutes. The total interval of possible flight times is 140 - 120 = 20 minutes. Thus, the probability is 10/20 or 0.50.
B. A flight over 10 minutes late means the flight time would be greater than 135 minutes (125 + 10). The interval of being more than 10 minutes late is 140 - 135 = 5 minutes. Hence, the probability is 5/20 or 0.25.
C. The expected flight time for a uniformly distributed random variable is the average of the minimum and maximum values, so it would be (120 + 140)/2 = 130 minutes.