Question

Delta airlines quotes a flight time of four hours, three minutes for a particular flight. suppose we believe that actual flight times are uniformly distributed between four hours and four hours, twelve 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 three minutes late.

(c) what is the probability that the flight will be no more than six minutes late.

(d) what is the expected flight time in minutes.

Answer 1

4 hours = 240 minutes and 4 hours 12 minutes = 252 minutes

(a) The pdf is attached below.

(b) To be no more than 3 minutes late, when the actual time is 4 hours, 3 minutes.

= 3 + 3 / 12 - 0 = 6 / 12 = 0.5

(c) To be no more than 6 minutes late, when the actual time is 4 hours, 3 minutes.

= 3 + 6 / 12 - 0 = 9 / 12 = 0.75

(d) Expected time = (a + b) / 2 = (252 + 240) / 2 = 492 / 2 = 246 minutes = 4 hours and 6 minutes