Problem
A farmer plants a crop in the spring and plans to sell 1.5M bushels to the market at harvest in 180 days. The farmer expects the price distribution in 180 days to have an expected value of $3.50/bu and a standard deviation of $0.45/ bu. Assuming the distribution is normal.
i. Determine the expected value and standard deviation of the famer's revenue from this sale in 180 days.
ii. What level of revenue would correspond to the worst 5% outcome?