However, John Junior was concerned that hisfather’s assumptions about the harvest did not captureall of the risks that the farm faced. After someprodding, John Junior was able to get his father toadmit that his forecasts were not always right, andJohn Senior provided John Junior with data aboutactual market prices and harvest yields in the past(Exhibit 1). John Junior noted with some concern thathis father’s forecast for the upcoming harvest wassimply the mean of the past ten years’harvests. Inaddition to the simple analysis his dad had asked himto do, John Junior decided to model the farm’sprofitability, factoring in uncertainty about how manytons of apples would actually be produced. He decidedthat production quantity was best approximated by anormal distribution with a mean of 743 tons (hisfather’s forecast) and standard deviation of 87 tons.

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