The scheduled arrival time for a daily flight from Boston to New York is 9:30 am

Question

The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:08 am and a late arrival time of 9:48 am.

a.

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.)

b.

What is the probability that a flight arrives late (later than 9:30 am)? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Explanation / Answer

a)

let 9:00 pm reprent t=0 minute

therefore arrvial time has uniform distirbution with parameter a =8 and b=48

therefore mean =(a+b)/2 =(8+48)/2 =28 minutes  

and std deviation =(b-a)/(12)1/2 =(48-8)/(12)1/2 =11.55

b)  probability that a flight arrives late =P(X>30) =1-P(X<30) =1-(30-8)/(48-8)=0.45

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