From past experience, a wheat farmer living in Manitoba, Canada finds that his annual profit (in Canadian dollars) 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. In the next year, let X be the farmer’s profit.
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.