PROPER USAGE OF NORMDIST AND NORMINV FUNCTIONS , AS WELL AS SKETCHES OF NORMAL DISTRIBUTION ILLUSTRATIONS, FOR THE PROBLEMS

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. Several Mercedes models are designed specifically to lure buyers away from BMW. In particular, Mercedes hopes their CLK will attract buyers who have been purchasing the BMW 328is. However, according to one recent automotive expert, the focus is still on luxury and comfort for Mercedes while BMW focuses on per- formance and driving dynamics. As of mid-1998, the average price for a CLK was $39,850 as compared to $34,745 for a 328is. Gas mileage for the CLK is 20 mpg in town and 27 mpg on the road as compared to 18 mpg in town and 26 mpg on the road for the 328is. DISCUSSION Suppose Mercedes-Benz is concerned that dealer prices of the CLK are not consistent and that while the average price is $39,850, the prices are actually normally distributed with a standard deviation of $2005. Suppose also that Mercedes-Benz believes that at $42,000, the CLK is priced out of the BMW 328is market. What percentage of the dealer prices are more than $42,000? The average price for a BMW 328is is $34,745. Suppose these prices are also normally distributed with a standard deviation of $1780. What percentage of BMW dealers are pricing the 328is at more than the average price for a CLK? What percentage of Mercedes-Benz dealers are pricing the CLK at less than the average price for a 328is? Suppose a dealer is selling a 328is for $37,059. What per- centage of Mercedes-Benz dealers price the CLK less than this? In terms of the CLK competing with the 328is pricewise, what do these data tell you