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 9:20 am and a late arrival time of 9:40 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.)

  Mean minutes  

Standard deviation minutes  

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.)   

Probability

Explanation / Answer

a)here 9:20 am to 9:40 am is toal 20 minutes and it should be represented as uniform distribution for paramters

a=0 to b=20.

a)mean minutes =(a+b)/2 =(0+20)/2 =10 minutes

std deviation =(b-a)/(12)1/2 =(20-0)/(12)1/2 =5.77 minutes

b) as 9:30 lies at 10 minues in our uniform distribution interal.

hence  probability that a flight arrives late P(X>10)=(20-10)/(20-0) =10/20 =0.50

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