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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