SOLUTION: Dear Tutor, I have always had trouble with probability, and I am faced with the following question: Delta Airlines quotes a flight time of 2hrs and 5 minutes for its flights

Question 290906: Dear Tutor,
I have always had trouble with probability, and I am faced with the following question:
Delta Airlines quotes a flight time of 2hrs and 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 120 to 140 minutes.
a. What is the probability that the flight will be more than 10 minutes late?
b. What is the expected flight time?
If you could answer one, or both parts of this question I would greatly appreciate it!!!
Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Delta Airlines quotes a flight time of 2hrs and 5 minutes (125 minutes) for its flights from Cincinnati to Tampa.
Suppose we believe that actual flight times are uniformly distributed between 120 to 140 minutes.
a. What is the probability that the flight will be more than 10 minutes late?
---
At least 10 minutes late is a flight of at least 135 minutes
If flight times range from 120 to 140 minutes, 6*sigma = 20
and sigma = 10/3
------------
Using the airlines schedule predictions,
find the probability flight time >= 135 min,
Find z(135) = (135-125)/(10/3) = 10/(10/3) = 3
Then P(x>= 135) = P(z> 3) = 0.00135
-----------------------------------------
b. What is the expected flight time?
Based on our observed times, expected flight time
is the average flight time = (140+120)/2 = 130 minutes.
==========================================
Cheers,
Stan H.
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