Question: 17. A sales manager is asked to forecast the total sales of his division for a forth coming period of time. He feels that his

17. A sales manager is asked to forecast the total sales of his division for a forth¬

coming period of time. He feels that his loss function is linear as a function of the difference between his estimate and the true value, but he also feels that an error of overestimation is three times as serious as an error of under¬

estimation (given that the magnitude of the errors is equal). This is because his superiors will criticize him if the division does worse than he predicts, but they will be happy if the division does better than predicted and will be less likely to be concerned about an error in predicting. If his actual judg¬

ments can be represented by a normal distribution with mean 50,000 and standard deviation 10,000, what value should he report as his forecast of sales?

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