32 The automobile industry sold 657,000 vehicles in the United States during Jan

Question

32 The automobile industry sold 657,000 vehicles in the United States during January 2009 (The Wall Street Journal, February 4, 2009). This volume was down 37% from January 2008 as economic conditions continued to decline. The Big Three U.S. automakers-General Motors, Ford, and Chrysler-sold 280,500 vehicles, down 48% from January 2008, A summary of sales by automobile manufacturer and type of vehicle sold is shown in the following table. Data are in thousands of vehicles. The non-U.S. manufacturers are led by Toyota, Honda, and Nissan. The category Light Truck includes pickup, minivan, SUV, and crossover model:s Type of Vehicle Car Light Truck 87.4 U.S Non-U.S. 228.5 193.1 148.0 Manufacturer a. Develop a joint probability table for these data and use the table to answer the remain- b. What are the marginal probabilities? What do they tell you about the probabilities c. If a vehicle was manufactured by one of the U.S. automakers, what is the probability d. If a vehicle was not manufactured by one of the U.S. automakers, what is the prob- e. If the vehicle was a light truck, what is the probability that it was manufactured by one f. What does the probability information tell you about sales? ing questions. associated with the manufacturer and the type of vehicle sold? that the vehicle was a car? What is the probability it was a light truck? ability that the vehicle was a car? What is the probability it was a light truck? of the U.S. automakers?

Explanation / Answer

a. original table:

joint probability table:

b. Marginal probabilities:

c. P [ vehicle was US as well as car ] =

P [ vehicle was US and light truck ] = 0.29391172

d. P [ not manufactured by US and it is car ] = 0.347793

P [ not manufactured by US and it is light truck ] =

0.225266362

Column1 Car Light truck Total US 87.4 193.1 280.5 non US 228.5 148 376.5 Total 315.9 341.1 657

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