Question

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.

Which of the following graphs accurately represents the probability density function for flight time in minutes?



SelectGraph #1Graph #2Graph #3Item 1

What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)?

What is the probability that the flight will be more than 10 minutes late (to 2 decimals)?

What is the expected flight time, in minutes?

Answer 1

As the time of the flight is uniformly distributed from 2 hours = 120 minutes and 140 minutes. Therefore we are given the distribution as:

$X \sim U[120,140]$

Therefore the probability density curve for X here would be given as:

$f(x) = \frac{1}{140-120} = 0.05$ which ranges from 120 to 140

Therefore the correct plot here would be given as:

b) Probability that the flight will be no more than 5 minutes late is computed here as:

$P(X < 130) = \frac{130-120}{140-120} = 0.5$

Therefore 0.50 is the required probability here.

c) Now the probability that the flight will be more than 10 minutes late is computed as:

$P(X > 135) = \frac{140-135}{140-120} = 0.25$

Therefore 0.25 is the required probability here.

c) The expected flight time here is computed as:

$E(X) = \frac{120+ 140}{2} = 130 \ minutes$