1. Profit and the weather 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 0.10of severe storm. Let X be the farmers 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 (ieP(), show work, and give probability to 4 decimal places.

c. Find the mean and standard deviation of the probability distribution of X. Provide the correctnotation, 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. (Hint: annual profit would change due to insurance costs and/or payout)