# Question

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.

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.

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