Mercedes and BMW have competed, head-to-head, for the market share of luxury cars for more than four decades. In 1959, BMW (Bayerische Motoren Werke) almost filed for bankruptcy and nearly exhausted Daimler-Benz, the Mercedes-Benz automaker. BMW was able to recover to such an extent that, in 1992, it surpassed Mercedes-Benz in worldwide sales. One of the reasons for BMW's success was its ability to sell models that were more luxurious than previous models, which focused on consumer quality and environmental responsibility. In particular, BMW aimed its sales pitch at the younger market, while Mercedes-Benz retained a more mature customer base.

In response to BMW's success, Mercedes-Benz has tried to change its image by launching several products, in an effort to attract younger buyers who are interested in sports cars and performance-oriented. BMW, influenced by Mercedes-Benz, is pushing for more refinement and comfort. In fact, an automotive expert says Mercedes-Benz wants to become BMW, and vice versa. However, according to an automotive expert, the focus is still on Mercedes-Benz luxury and comfort, while BMW focuses on performance and driving dynamics. Although each company produces many different models, two relatively comparable "coupe" cars are the BMW 3 Series Coup 335i and the Mercedes CLK350 Coup. In a recent year, the US domestic market price for the BMW 3 Series Coup 335i was and for the Mercedes-Benz CLK350 Coup was . The fuel consumption of both cars is around city, and highway.

Based on the above:

1. Suppose Mercedes is concerned that dealer prices for the CLK350 Coupe are not consistent and that, even if the average price is , actual prices are normally distributed with a standard deviation of . Suppose, too, that Mercedes believes that a , the CLK350 Coupe is priced outside the BMW 3 Series Coupe 335i market. What percentage of the dealer prices for the Mercedes CLK350 Coupe is (are) more than and therefore outside the BMW 3 Series Coupe 335i market? The average price of a BMW 3 Series Coup 335i is . Suppose these prices are also normally distributed with a standard deviation of . What percentage of BMW dealers are valuing the BMW 3 Series Coup 335i at a price above the average of a Mercedes CLK350 Coup? What could this mean for BMW if dealers were valuing the 3 Series Coupe 351 at this level? What percentage of Mercedes dealers are valuing the CLK350 pair at a price below the average price of a BMW 3 Series Coup 335i?

1. Suppose that the gasoline mileage rates, on the road, for both cars are evenly distributed in a range Mercedes and BMW have competed, head-to-head, for the market share of luxury cars for more than four decades. In 1959, BMW (Bayerische Motoren Werke) almost filed for bankruptcy and nearly exhausted Daimler-Benz, the Mercedes-Benz automaker. BMW was able to recover to such an extent that, in 1992, it surpassed Mercedes-Benz in worldwide sales. One of the reasons for BMW's success was its ability to sell models that were more luxurious than previous models, which focused on consumer quality and environmental responsibility. In particular, BMW aimed its sales pitch at the younger market, while Mercedes-Benz retained a more mature customer base.

In response to BMW's success, Mercedes-Benz has tried to change its image by launching several products, in an effort to attract younger buyers who are interested in sports cars and performance-oriented. BMW, influenced by Mercedes-Benz, is pushing for more refinement and comfort. In fact, an automotive expert says Mercedes-Benz wants to become BMW, and vice versa. However, according to an automotive expert, the focus is still on Mercedes-Benz luxury and comfort, while BMW focuses on performance and driving dynamics. Although each company produces many different models, two relatively comparable "coupe" cars are the BMW 3 Series Coup 335i and the Mercedes CLK350 Coup. In a recent year, the US domestic market price for the BMW 3 Series Coup 335i was and for the Mercedes-Benz CLK350 Coup was . The fuel consumption of both cars is around city, and highway.

Based on the above:

1. Suppose Mercedes is concerned that dealer prices for the CLK350 Coupe are not consistent and that, even if the average price is , actual prices are normally distributed with a standard deviation of . Suppose, too, that Mercedes believes that a , the CLK350 Coupe is priced outside the BMW 3 Series Coupe 335i market. What percentage of the dealer prices for the Mercedes CLK350 Coupe is (are) more than and therefore outside the BMW 3 Series Coupe 335i market? The average price of a BMW 3 Series Coup 335i is . Suppose these prices are also normally distributed with a standard deviation of . What percentage of BMW dealers are valuing the BMW 3 Series Coup 335i at a price above the average of a Mercedes CLK350 Coup? What could this mean for BMW if dealers were valuing the 3 Series Coupe 351 at this level? What percentage of Mercedes dealers are valuing the CLK350 pair at a price below the average price of a BMW 3 Series Coup 335i?

2. Suppose that the gasoline mileage rates, on the road, for both cars are evenly distributed in a range of a. What proportion of these cars would fall in the range of a ? Calculate the proportion of cars getting more than . What proportion of cars would get less than ?

3. Suppose an average of CLK is sold at a dealership each (during a day of exposure) and that sales are distributed by Poisson. The following probabilities produced indicate the occurrence of different times between sales based on this information. Study the result and interpret for the sellers. For example, what is the probability that less than an hour will elapse between sales? What is the likelihood that it will be more than a day (12-hour day) before the next sale after a car has been sold? What can dealer managers do with such information? How can you help in staffing? How can that information be used as a device to track the impact of advertising? Is there a chance that these odds will change during the year? If so, why?

of a. What proportion of these cars would fall in the range of a ? Calculate the proportion of cars getting more than . What proportion of cars would get less than ?

4. Suppose an average of CLK is sold at a dealership each (during a day of exposure) and that sales are distributed by Poisson. The following probabilities produced indicate the occurrence of different times between sales based on this information. Study the result and interpret for the sellers. For example, what is the probability that less than an hour will elapse between sales? What is the likelihood that it will be more than a day (12-hour day) before the next sale after a car has been sold? What can dealer managers do with such information? How can you help in staffing? How can that information be used as a device to track the impact of advertising? Is there a chance that these odds will change during the year? If so, why?