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 9:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:17 am and a late arrival time of 9:42 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 9:25 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Solution

Here, x= 9:35 am = 9*60+25 minutes = 565 minutes.

Here for the uniform distribution, a = 9:17 am = 557 min. & b = 9:42 am = 582 min.

(a) Mean = (a+b)/2 = 569.5 minutes.

Standard Deviation =   \\(\\sqrt{(b-a)^{2}/12}\\)  

= 7.21 minutes.

(b) P robability that a flight arrives late (later than 9:25 am) = 1 - (x-a)/(b-a)

= 0.5