The scheduled arrival time for a daily flight from Boston to

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 9:13 am and a late arrival time of 9:53 am.

After converting the time data to a minute scale, calculate the mean and the standard deviation for the distribution. (Round your answers to 2 decimal places.)

What is the probability that a flight arrives late (later than 9:35 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Solution

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 9:13 am and a late arrival time of 9:53 am.

a.       

After converting the time data to a minute scale, calculate the mean and the standard deviation for the distribution. (Round your answers to 2 decimal places.)

Converting early arrival time of 9:13 am and a late arrival time of 9:53 am., this becomes

uniform distribution with a=0, b=40

Expectation = (a+b)/2 = 20

Variance = (b-a)²/12 = 133.3333

Standard deviation = 11.5470

Mean            20 minutes

Standard deviation 11.55   minutes

b.        

What is the probability that a flight arrives late (later than 9:35 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

9.35 - 9.13 =22 minutes

P(later than 9:35 am ) = P( X>22 ) = 0.45

Probability = 0.45