Questions: MotoWin Auto Superstore is thinking about offering a two-year limited warranty for 928 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 13,800. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car. 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.

MotoWin Auto Superstore is thinking about offering a two-year limited warranty for 928 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 13,800. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car. 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.
Transcript text: MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $\$ 928$ 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 $\$ 13,800$. Suppose that under the warranty, there is a $7 \%$ chance that MotoWin would have to replace the car one time and a $93 \%$ chance they wouldn't have to replace the car. 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 $\square$ dollars on each warranty sold. MotoWin can expect to lose money from offering these warranties. In the long run, they should expect to lose $\square$ dollars on each warranty sold. MotoWin should expect to neither make nor lose money from offering these warranties.
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Solution

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Solution Steps

Step 1: Calculate the Expected Cost of Replacement

To determine the expected cost of replacing a car under the warranty, we calculate the mean of the distribution of possible outcomes:

\[ \text{Mean} = 0 \times 0.93 + 13800 \times 0.07 = 966.0 \]

Thus, the expected cost of replacement is \( \$966.0 \).

Step 2: Calculate the Expected Profit per Warranty Sold

Next, we find the expected profit per warranty sold by subtracting the expected cost from the price of the warranty:

\[ \text{Expected Profit} = 928 - 966.0 = -38.0 \]

This indicates that MotoWin expects to incur a loss of \( \$38.0 \) for each warranty sold.

Step 3: Determine Financial Outcome

Since the expected profit is negative, we conclude that MotoWin can expect to lose money from offering these warranties. Specifically, in the long run, they should expect to lose \( \$38.0 \) dollars on each warranty sold.

Final Answer

MotoWin can expect to lose money from offering these warranties. In the long run, they should expect to lose \( \boxed{38.0} \) dollars on each warranty sold.

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