Question

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati toTampa. Suppose we believe that actual flight times are uniformly distributed between2 hours and 2 hours, 20 minutes.a. Show the graph of the probability density function for flight time.b. What is the probability that the flight will be no more than 5 minutes late?c. What is the probability that the flight will be more than 10 minutes late?d. What is the expected flight time?

Answer 1

a) The graph of the probability density function for flight time is shown below.

b) 1/2

c) 0

d) 130 minutes

Explanation:

Let's deal with the flight times in minutes instead of hours, and let T be the random variable that represents the flight time. T is uniformly distributed between 120 minutes and 140 minutes. The probability density function for T is given by

`f(t)=(1)/(140-120)=(1)/(20)` for t in [120, 140]

a) The graph of the probability density function for flight time is shown below.

Delta Airlines quotes a flight time of 125 minutes for its flights from Cincinnati to Tampa.

b) The probability that the flight will be no more than 5 minutes late is given by

`P(T \leq 125 + 5) = P(T \leq 130) = \int\limits_(120)^(130)(1)/(20)dt = (1)/(20)(130-120)= (1)/(20)(10) = (1)/(2)`

c) The probability that the flight will be more than 10 minutes late is given by

`P(T \geq 125 + 10) = P(T \geq 135) = 0` because the probability density function is zero for t outside of [120, 140]

d) The expected flight time is given by
`E(T) = (120+140)/(2) = (260)/(2) = 130` minutes