# C if it writes 10000 of these policies what are the

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c) If it writes 10,000 of these policies, what are the mean and standard deviation of the annual profit? d) Do you think the company is likely to be profitable? Explain. Hint: draw and label a normal curve with the information calculated in part (c). e) What assumptions underlie your analysis? Can you think of circumstances under which the assumption might be violated? Explain. 5. A farmer has 100 lb of apples and 50 lb of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of \$0.50 and a SD of \$0.20. Similarly, for a pound of potatoes, the mean price is \$0.30 and the SD is \$0.10. It also costs him \$2.00 to bring all the produce to the market. Assume that he’ll be able to sell all of each type of produce at the day’s price. a) Define your random variables. b) Use your defined random variables in part (a) to express the farmer’s net income. c) Find the mean of the farmer’s net income. d) Find the standard deviation of the farmer’s net income. e) Do you need to make any assumptions in calculating the mean? f) Do you need to make any assumptions in calculating the standard deviation? Policyholder outcome Payout, Y Probability P(Y = y) Death \$100,000 10000 1 Disabled \$50,000 10000 2 Neither \$0 10000 9997 R=# of red lights 0 1 2 3 P(R = r) .05 .20 .30 .45

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• Fall '19
• Variance, Probability theory, probability density function
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