In response to BMW$\text{'}$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 $335$i and the Mercedes CLK$350$ Coupe. In a recent year, the national U$.$S$.$ market price for the BMW $3$ Series Coupe $335$i was $$39,368$ and for the Mercedes CLK$350$ Couple was $$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 CLK$350$

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 $$43,000,$ the CLK$350$ Coupe is priced out of the BMW $3$ Series Coupe $335$ market. What percentage of the dealer prices for the Mercedes CLK$350$ Coupe is more than $$43,000$ and hence priced out of the BMW $3$ Series Coupe $335$i market? Round your answer to $3$ decimal places. For example, if your answer is $0\mathrm{.}81233$ enter $0\mathrm{.}812$

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