Question

Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes. Letting the time unit be one minute,

(a) Calculate the mean flight time and the standard deviation of the flight time. (Round your answers to 4 decimal places.) μx σx

(b) Find the probability that the flight time will be within one standard deviation of the mean. (Round your answer to 5 decimal places.) P =

The ones that are coming up are answering different questions.

Answer 1

If X ~ Uniform(a,b)
Then mean, E[X] = (a+b)/2
and Variance, Var(x) = 1/12 x(b-a)²
Here flight time T ~ Uniform(2, 2:20)
(a)
Mean flight time: E[X] = (2:00 + 2:20) / 2 = 2:10 i.e 2 hours 10 minutes
Var(T) = 1/12 x (2:20 - 2:00)² = 1/12 x 400 = 100/3 = 33.33 minutes
Standard deviation SD(T) = 5.77 minutes

(b)
Flight time within 1 std. deviation i.e flight time is b/w 2:10 hours - 5.77 minutes and 2:10 hours - 5.77 minutes
P(2:10 - 5.77 < T < 2:10 + 5.77) = (5.77 - (-5.77)) / 20 = 0.577