Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two

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.) x x (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 =

Explanation / Answer

Answer:

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= 2 hours= 120 minutes

b= 2 hours 20 minutes= 140 minutes

x =Expectation = (a + b)/2 = 130

Variance = (b - a)2/12 = 33.3333

x = Standard deviation = 5.7735

(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 =

within one standard deviation of the mean is within ( 130-5.7735, 130+5.7735).

P( 124.2265<x<135.7735)= P( x <135.7735) – P( x < 124.2265)

= 0.78868- 0.21133

=0.57735

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