QuestionMotoWin Auto Superstore is thinking about offering a two-year limited warranty for on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin . Suppose that under the warranty, there is a chance that MotoWin would have to replace the car one time and a chance they wouldn't have to replace the car.
(If necessary, consult a list of formulas.)
If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much?
To answer, take into account the price of the warranty and the expected value of the cost from replacing the car.
MotoWin can expect to make money from offering these warranties.
In the long run, they should expect to make dollars on each warranty sold.
MotoWin can expect to lose money from offering these warranties.
In the long run, they should expect to lose dollars on each warranty sold.
MotoWin should expect to neither make nor lose money from offering these warranties.
Studdy Solution
STEP 1
1. The cost of the warranty is .
2. The cost to replace the car is .
3. There is a probability that MotoWin will have to replace the car.
4. There is a probability that MotoWin will not have to replace the car.
STEP 2
1. Calculate the expected cost of replacing the car.
2. Determine the expected profit or loss from the warranty.
STEP 3
Calculate the expected cost of replacing the car using the formula for expected value:
\[
\text{Expected Cost} = (0.07 \times 13,600) + (0.93 \times 0) $
\[
\text{Expected Cost} = 952 $
STEP 4
Calculate the expected profit or loss by subtracting the expected cost from the warranty price:
\[
\text{Profit/Loss} = 952 - 952 $
\[
\text{Profit/Loss} = 0 $
MotoWin should expect to neither make nor lose money from offering these warranties.
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