Suppose Mercedes is concerned that dealer prices of the C350 Coupe are not consi

Question

Suppose Mercedes is concerned that 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 $2981.

a. 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?

b. 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 $2367. What percentage of BMW dealers is pricing the BMW 3 Series Coupe 335i at more than the average price of a Mercedes C350 Coupe?

c. What might this mean to BMW if dealers were pricing the 3 Series Coupe 335i at this level?

d. What percentage of Mercedes dealers is pricing the C350 Coupe at less than the average price of a BMW 3 Series Coupe 335i?

Explanation / Answer

a) P(X>44000) =1-P(X<44000)=1-P(Z<(44000-45493)/2981)=1-P(Z<-0.50)=1-0.3082=0.6918 or 69.18%

b)P(X>45493)=1-P(X<45493)=1-P(Z<(45493-41022)/2367)=1-P(Z<1.8889)=1-0.9705=0.0295 or 2.95%

c)that is an unusual event for BMW and they have to take care of the situation to retain the market

d)P(X<41022)=P(Z<(41022-45493)/2981)=P(Z<-1.5)=0.0668 or 6.68%

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