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An auto dealer believes that demand for 2024 model cars will be normally distributed with a mean of 200 and a standard deviation of 30.

An auto dealer believes that demand for 2024 model cars will be normally distributed with a mean of 200 and a standard deviation of 30. His cost of receiving a car is $25,000, and he sells the car for $40,000. Half of all cars not sold at full price can be sold for $30,000. He is considering ordering 200, 220, 240, 269, 280, or 300 cars. Which order quantity has the highest expected (average) profit? Which has the lowest standard deviation in profit?

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