According to the Agricultural Department, a wheat farmer finds that his annual profit is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is a severe storm that destroys much of his crop. Weather bureau records indicate that the probability is 0.70 of typical weather, 0.20 of unusually dry weather, and 0.10 of a severe storm. Let X denote the farmer's profit next year. (a) Construct a table with the probability distribution of X. (b) What is the probability that the profit is $50,000 or less? (c) Find the mean of the probability distribution of X. Interpret. (d) Suppose the farmer buys insurance for $3000 that pays him $20,000 in the event of a severe storm that destroys much of the crop and pays nothing otherwise. Find the probability distribution of his profit. Find the mean and summarize the effect of buying this insurance.