Question

Suppose that an airline quotes a flight time of 135 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 115 and 155 minutes. Letting the time unit be one minute,

(a) Write the formula for the probability curve of x.

(c) Find P(139 < x < 141). (Round your answer to 4 decimal places.)

(d) Find the probability that a randomly selected flight between the two cities will be at least 5 minutes late. (Round your answer to 4 decimal places.)

Answer 1

Solution:

Given:  an airline quotes a flight time of 135 minutes between two cities.

the actual flight time between the two cities, x, is uniformly distributed between 115 and 155 minutes.

X ~ Uniform( a = 115 minutes, b = 155 minutes)

Part a) Write the formula for the probability curve of x.

For a continuous Uniform distribution with parameters (a,b), probability density function ( pdf) is given by:

that is:

Part c) Find P(139 < x < 141).

P(139 < x < 141) = P( X < 141 ) - P( X < 139)

Use following cumulative density function of uniform distribution.

thus

P(139 < x < 141) = P( X < 141 ) - P( X < 139)

Part d) Find the probability that a randomly selected flight between the two cities will be at least 5 minutes late

Find :

P( X > 135+5) =............?

P( X > 140)  =..............?

P( X > 140)  =1 - P(X < 140 )