Question 1 Uniform Probability Distribution (60 – 70 mins)

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from

Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly

distributed between 2 hours and 2 hours, 20 minutes.

1. Give a mathematical expression for the probability density function of flight time and the expected value and variance of the distribution;

2. Create a scatter graph using dynamic process learnt in the previous sessions to show the uniform probability distribution graphically, then answer the below questions:

a. What is the probability that the flight will be no more than 5

minutes late?

b. What is the probability that the flight will be more than 10 minutes late?