Question

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 Couple was $44,520. Gas mileage for both of these cars is around 17 mpg in town and 25 mpg on the highway.

Question 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, 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? Round your answer to 3 decimal places.

Answer 1

We need to find the Z statistic for the price of CLK350 Coupe at price value of $43,000 based on the average and standard deviation values.

Percentage of the dealer prices for the Mercedes CLK350 Coupe that is more than $43,000 and hence priced out of the BMW 3 Series Coupe 335i market is therefore obtained as

So about 69.5% Mercedes CLK350 Coupe are priced out of the BMW 3 Series Coupe 335i market