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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?

c. What is the probability that the flight will be between 4 and 8

minutes late?

d. In a month of 200 flight journeys finished, how many should have arrived 5 minutes or less earlier?

Question 2 Normal Distribution

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55.

2 a. Draw on a piece of paper the Normal Distribution curve and mark the Mean and 1 unit standard deviation to each side of the Mean.

2 b. Show the Probability Density Function to your tutor and point it on your graph.

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