Question

An airline quotes a flight time of 2 hours, 5 minutes for its flights from City A to B.

Suppose actual flight times are uniformly distributed between 2 hours and 2 hours, 20

minutes. (i) What is the probability that a flight will be no more than five minutes late?, (ii)

What is the probability that a flight will be more than 10 minutes late?​

Answer 1

Given : An airline quotes a flight time of 2 hours, 5 minutes for its flights from City A to B. Suppose actual flight times are uniformly distributed between 2 hours and 2 hours, 20

To find :  probability that a flight will be no more than five minutes late

probability that a flight will be more than 10 minutes late

Solution:

flight times are uniformly distributed between 2 hours and 2 hours, 20

Mean Flight time = (2 +  2hr 20 mins)/2  = 2 hr 10 mins

Range = 2hr 20 mins - 2 hr = 20 mins

Range = 6.8 SD

=> SD = 20/6.8

probability that a flight will be no more than five minutes late

=> Flight will be between 2 hr to 2 hr 15 mins

Z score =  (Value - Mean)/SD   = 5/(20/6.8)  = 1.7

Z score = 1.7 => 0.9554

probability that a flight will be no more than five minutes late =  0.9554

probability that a flight will be more than 10 minutes late

actual flight times are uniformly distributed between 2 hours and 2 hours, 20

Hence probability = 0  that flight will be more than 10 mins Late

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