Mercedes and BMW have been competing headtohead 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 DaimlerBenz, the maker of MercedesBenz 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 respon sibility. 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, performanceoriented cars. BMW, influenced by Mercedes, is pushing for more refinement and comfort. In fact, one auto motive 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 Couple was $44,520. Gas mileage for both of these cars is around 17 mpg in town and 25 mpg on the highway. 1. Suppose that highway gas mileage rates for both of these cares 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? 2. Suppose that in one dealership an average of 1.37 CLKs is sold every 3 hours (during 12hour showroom day) and hat sales are Poisson distributed. The following Excel produced probabilities indicate the occurrence of differ ent intersales times based on this information. Study the output and interpret it for the salespeople. For example, what is the probability that less than an hour will elapse between sales? What is the probability that more than a day (12hour 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 3Hour Time Frame 0.167 0.333 0.667 1 2 3 4 5 Comulative Exponential Probabilities from Left 0.2045 0.3663 0.5990 0.7459 0.9354 0.9836 0.9958 0.9989