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Delta Airlines quotes a flight time of 125 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 120 minutes and 140 minutes

A. What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)?
B. What is the probability that the flight will be more than 10 minutes late (to 2 decimals)?
C. What is the expected flight time, in minutes?

User RobEarl
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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.

User Parul
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