From past experience a wheat farmer living Manitoba Canada f

From past experience, a wheat farmer living Manitoba, Canada finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather if 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 severe storm. Let X be the farmer’s profit in the 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? Provide the probability statement (ie P(...), show work, and give probability to 4 decimal places.

c. Find the mean and standard deviation of the probability distribution of X. Provide the correct notation, value to 3 decimal places, and correct units.

d. Suppose the farmer buys insurance for $3,000 that pays him $20,000 in the event of a severe storm that destroys much of the crop and pays nothing other-wise. Find the probability distribution of his profit. Find the mean, and summarize the effect of buying this insurance.

Solution