Question

1.       A researcher tells you that flights between two cities in the United States are uniformly distributed with arrival times that vary between 4 hours and 4 hours 30 minutes, with a mean of 4 hours 15 minutes.

a.       Sketch out a related graph, being sure to label the base and the height appropriately. (10 pts.)

b.       What is the probability of a randomly chosen flight between these two cities arriving in less than 4 hours 10 minutes? (15 pts.)

c.       What is the probability of a randomly chosen flight between these two cities arriving in more than 4 hours 20 minutes? (15 pts.)

d.       You share this test problem with a pilot friend of yours. S/he is very surprised at the idea that such flights would actually be distributed uniformly. Please explain why we might expect such an objection. (10 pts.)

Answer 1

a) Lower limit = 4.0 hours

Upper limit = 4 hours 30 minutes = 4.50 hours

Let's use minitab:

Click on graph >>>Probability Distribution plot..Select first image>>> OK

Distribution: Uniform

Lower endpoint : 4

Upper endpoint : 4.5

Then click on OK so we get the following output

b) We want to find the probability of a randomly chosen flight between these two cities arriving in less than 4 hours 10 minutes

Mathematically P(X < 4.166667) = (4.166667 - 4) / (4.5 - 4) = 0.333333

c) the probability of a randomly chosen flight between these two cities arriving in more than 4 hours 20 minutes.

P(X > 4.333333) = (4.5 - 4.333333)/(4.5 - 4) = 0.333333