The scheduled arrival time for a daily flight from Boston to New York is 9:35 am

Question

The scheduled arrival time for a daily flight from Boston to New York is 9:35 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:12 am and a late arrival time of 9:46 am.

After converting the time data to a minute scale, calculate the mean and the standard deviation of the distribution. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

What is the probability that a flight arrives late (later than 9:35 am)? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

The scheduled arrival time for a daily flight from Boston to New York is 9:35 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:12 am and a late arrival time of 9:46 am.

Explanation / Answer

Answer to the question as below:

x= 35 minutes
a = 12 minutes
b = 46 minutes

a. Mean = b-a/2 = 46-12/2 = 17 minutes So, 9:17 am is the mean time
Stdev = (b-a)^2/12 = (46-12)^2/12 = 96.33 minutes

b. P( flight arrives late) = P(X>9:35) =1- ( 35-12 / 46-12 )= 1-.6765
So, there is 32.35% probability to be later than 9:35am

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