# Question

In 1959, BMW (Bayerische Motoren Werke) almost went bankrupt and nearly sold out to Daimler-Benz, the maker of Mercedes-Benz cars. BMW was able to recover to the point that in 1992 it passed Mercedes in worldwide sales. Among the reasons for BMW’s success was its ability to sell models that were more luxurious than previous models but still focused on consumer quality and environmental responsibility. In particular, BMW targeted its sales pitch to the younger market, whereas Mercedes retained a more mature customer base.

In response to BMW’s success, Mercedes has been trying to change its image by launching several products in an effort to attract younger buyers who are interested in sporty, performance-oriented cars. BMW, influenced by Mercedes, is pushing for more refinement and comfort. In fact, one automotive expert says that Mercedes wants to become BMW, and vice versa. However, according to one recent automotive expert, the focus is still on luxury and comfort for Mercedes while BMW focuses on performance and driving dynamics. Even though each company produces many different models, two relatively comparable coupe automobiles are the BMW 3 Series Coupe 335i and the Mercedes C350 Coupe. In a recent year, the national U.S. market price for the BMW 3 Series Coupe 335i was $41,022 and for the Mercedes C350 Coupe $45,493. Gas mileage for both of these cars is around 17 mpg in town and 25 mpg on the highway.

Discussion

1. Suppose Mercedes is concerned those dealer prices of the C350 Coupe are not consistent and that even though the average price is $45,493, actual prices are normally distributed with a standard deviation of $2,981.Suppose also that Mercedes believes that at $44,000, the C350 is priced out of the BMW 3 Series Coupe 335i market. What percentage of the dealer prices for the Mercedes C350 Coupe is more than $44,000 and hence priced out of the BMW 3 Series Coupe 335i market? The average price for a BMW 3 Series Coupe 335i is $41,022. Suppose these prices are also normally distributed with a standard deviation of$2,367.What percentage of BMW dealers is pricing the BMW 3 Series Coupe 335i at more than the average price of a Mercedes C350 Coupe? What might this mean to BMW if dealers were pricing the 3 Series Coupe 335i at this level? What percentage of Mercedes dealers is pricing the C350 Coupe at less than the average price of a BMW 3 Series Coupe 335i?

2. Suppose that highway gas mileage rates for both of these cars are uniformly distributed over a range of from 20 to 30 mpg. What proportion of these cars would fall into the 22 to 27 mpg range? Compute the proportion of cars that get more than 28 mpg. What proportion of cars would get less than 23 mpg?

3. Suppose that in one dealership an average of 1.37 Mercedes CLKs is sold every 3 hours (during a 12-hour showroom day) and that sales are Poisson distributed.

The following Excel-produced probabilities indicate the occurrence of different inter-sales times based on this information. Study the output and interpret it for the sales people. For example, what is the probability that less than an hour will elapse between sales? What is the probability that more than a day (12-hour day) will pass before the next sale after a car has been sold? What can the dealership managers do with such information? How can it help in staffing? How can such information be used as a tracking device for the impact of advertising? Is there a chance that these probabilities would change during the year? If so, why?

Portion of 3-Hour Cumulative Exponential

Time Frame ....... Probabilities from Left

0.167 .......... 0.2045

0.333 .......... 0.3663

0.667 .......... 0.5990

1 ........... 0.7459

2 ........... 0.9354

3 ........... 0.9836

4 ........... 0.9958

5 ........... 0.9989

In response to BMW’s success, Mercedes has been trying to change its image by launching several products in an effort to attract younger buyers who are interested in sporty, performance-oriented cars. BMW, influenced by Mercedes, is pushing for more refinement and comfort. In fact, one automotive expert says that Mercedes wants to become BMW, and vice versa. However, according to one recent automotive expert, the focus is still on luxury and comfort for Mercedes while BMW focuses on performance and driving dynamics. Even though each company produces many different models, two relatively comparable coupe automobiles are the BMW 3 Series Coupe 335i and the Mercedes C350 Coupe. In a recent year, the national U.S. market price for the BMW 3 Series Coupe 335i was $41,022 and for the Mercedes C350 Coupe $45,493. Gas mileage for both of these cars is around 17 mpg in town and 25 mpg on the highway.

Discussion

1. Suppose Mercedes is concerned those dealer prices of the C350 Coupe are not consistent and that even though the average price is $45,493, actual prices are normally distributed with a standard deviation of $2,981.Suppose also that Mercedes believes that at $44,000, the C350 is priced out of the BMW 3 Series Coupe 335i market. What percentage of the dealer prices for the Mercedes C350 Coupe is more than $44,000 and hence priced out of the BMW 3 Series Coupe 335i market? The average price for a BMW 3 Series Coupe 335i is $41,022. Suppose these prices are also normally distributed with a standard deviation of$2,367.What percentage of BMW dealers is pricing the BMW 3 Series Coupe 335i at more than the average price of a Mercedes C350 Coupe? What might this mean to BMW if dealers were pricing the 3 Series Coupe 335i at this level? What percentage of Mercedes dealers is pricing the C350 Coupe at less than the average price of a BMW 3 Series Coupe 335i?

2. Suppose that highway gas mileage rates for both of these cars are uniformly distributed over a range of from 20 to 30 mpg. What proportion of these cars would fall into the 22 to 27 mpg range? Compute the proportion of cars that get more than 28 mpg. What proportion of cars would get less than 23 mpg?

3. Suppose that in one dealership an average of 1.37 Mercedes CLKs is sold every 3 hours (during a 12-hour showroom day) and that sales are Poisson distributed.

The following Excel-produced probabilities indicate the occurrence of different inter-sales times based on this information. Study the output and interpret it for the sales people. For example, what is the probability that less than an hour will elapse between sales? What is the probability that more than a day (12-hour day) will pass before the next sale after a car has been sold? What can the dealership managers do with such information? How can it help in staffing? How can such information be used as a tracking device for the impact of advertising? Is there a chance that these probabilities would change during the year? If so, why?

Portion of 3-Hour Cumulative Exponential

Time Frame ....... Probabilities from Left

0.167 .......... 0.2045

0.333 .......... 0.3663

0.667 .......... 0.5990

1 ........... 0.7459

2 ........... 0.9354

3 ........... 0.9836

4 ........... 0.9958

5 ........... 0.9989

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