1 Profit and the weather From past experience a wheat farmer

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 0.10 of severe storm. Let X be the farmer’s profit in the next year. a. (2 pts) Construct a table with the probability distribution of X. b. (2 pts) 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. (2 pts) Find the mean and standard deviation of the probability distribution of X. Provide the correct notation, value to 3 decimal places, and correct units.

Solution

A)

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B)

P(50000 or less) = P(50000) + P(20000) = 0.20 + 0.10 = 0.30 [ANSWER]

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c)

Consider the table:

Thus,          
          
E(x) = Expected value = mean =    68000   [ANSWER, MEAN]  

Also,

Var(x) = E(x^2) - E(x)^2 =    396000000      

s(x) = sqrt [Var(x)] =    19899.74874   [ANSWER, STANDARD DEVIATION]