Mercedes and BMW have been competing head-to-head for market share in the luxury-car market for more than four decades. Back 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 their 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 CLK350 Coupe. In a recent year, the national U.S. market price for the BMW 3 Series Coupe 335i was $39,368 and for the Mercedes CLK350 Coupe was $44,520. Gas mileage for both of these cars is around 17 mpg in town and 25 mpg on the highway.
1. Suppose Mercedes is concerned that dealer prices of the CLK350 Coupe are not consistent and that even though the average price is $44,520, the actual prices are normally distributed with a standard deviation of $2,981. Suppose also that Mercedes believes that at $43,000, the CLK350 Coupe is priced out of the BMW 3 Series Coupe 335i market. What percentage of the dealer prices for the Mercedes CLK350 Coupe is more than $43,000 and hence priced out of the BMW 3 Series Coupe 335i market?
2. The average price for a BMW 3 Series Coupe 335i is $39,368. Suppose these prices are also normally distributed with a standard deviation of $2,367. What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price for a Mercedes CLK350 Coupe? What might this mean to BMW if dealers were pricing the 3 Series Coupe 335i at this level? What percentage of Mercedes dealers are pricing the CLK350 Coupe at less than the average price of a BMW 3 Series Coupe 335i?
3. Suppose that highway gas mileage rates for both of these cares are uniformly distributed over a range of 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?
4. Suppose that in one dealership an average of 1.37 CLK’s 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 intersales times based on this information. Study the output and interpret it for the salespeople.
a. What is the probability that less than an hour will elapse between sales?
b. What is the probability that more than a 12-hour day will pass before the next sale after a car has been sold?
Table of Excel produced probabilities:
Portion of 3-Hour
Time Frame Cumulative Exponential
Probabilities from Left
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