Questions: Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out 26,500 to the policy holder. Executives at Avicenna are considering offering these policies for 497 each. Suppose that for each holder of a policy there is a 2% chance they will experience property damage in the next five years and a 98% chance they will not. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose dollars on each policy sold. Avicenna should expect to neither make nor lose money from offering these policies.

Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out 26,500 to the policy holder. Executives at Avicenna are considering offering these policies for 497 each. Suppose that for each holder of a policy there is a 2% chance they will experience property damage in the next five years and a 98% chance they will not. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose dollars on each policy sold. Avicenna should expect to neither make nor lose money from offering these policies.
Transcript text: Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $\$ 26,500$ to the policy holder. Executives at Avicenna are considering offering these policies for $\$ 497$ each. Suppose that for each holder of a policy there is a $2 \%$ chance they will experience property damage in the next five years and a $98 \%$ chance they will not. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose $\square$ dollars on each policy sold. Avicenna should expect to neither make nor lose money from offering these policies.
failed

Solution

failed
failed

Solution Steps

To determine whether Avicenna will make or lose money from offering these insurance policies, we need to calculate the expected value of the payout and compare it to the price of the policy. The expected value (EV) of the payout is calculated by multiplying the probability of property damage by the payout amount and adding it to the probability of no damage multiplied by zero (since no payout is made in that case). Then, subtract the expected payout from the policy price to determine the expected profit or loss per policy.

Step 1: Calculate the Expected Payout

To find the expected payout, we use the formula for expected value: \[ \text{Expected Payout} = (\text{Probability of Damage} \times \text{Payout}) + (\text{Probability of No Damage} \times 0) \] Substituting the given values: \[ \text{Expected Payout} = (0.02 \times 26500) + (0.98 \times 0) = 530 \]

Step 2: Calculate the Expected Profit or Loss per Policy

The expected profit or loss per policy is calculated by subtracting the expected payout from the policy price: \[ \text{Expected Profit per Policy} = \text{Policy Price} - \text{Expected Payout} \] Substituting the given values: \[ \text{Expected Profit per Policy} = 497 - 530 = -33 \]

Step 3: Determine if Avicenna Will Make or Lose Money

Since the expected profit per policy is negative, Avicenna can expect to lose money on each policy sold. Specifically, they will lose \(-33\) dollars per policy.

Final Answer

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose \(\boxed{33}\) dollars on each policy sold.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Sophie is baking chocolate chip cookies for her friends. The recipe for one batch requires 2 1/3 cups of flour. Sophie wants to make 1 3/4 times the recipe to have enough cookies for everyone. How many cups of flour does she need in total?
failedAnswered
A runner completed a marathon in 3 hours and 34 minutes. What was her average speed, in meters per second? 1 marathon = 26.2 miles. 1 mile = 1.609 kilometers. 3.91 meters / second 1.27 meters / second 3.28 meters / second 7.34 meters / second
failedAnswered
Walter deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of 85,000 in 18 years. Assuming an APR of 3.1% compounded monthly, how much is interest earned? Round your answers to the nearest cent, if necessary.
failedAnswered
modulus of elasticity is a structure insensitive property [it is a unique property of a material- it is a property of the atomic bond in the material, and can not be altered by changing chemical composition or of a material] [this therefore means stiffness is structure property]
failedAnswered
Read this text from paragraph 3. (3) ... Roosevelt met up with John Muir and they spent three days camping alone in the Yosemite high country. Because of the impression Muir made upon Roosevelt, Yosemite National Park would be expanded and control of the park would be tumed back over to the federal government. Roosevelt would later go on to sign into law the Antiquities Act, which gives the President the power to proclaim an area of natural or historical value as public lands. Which excerpt supports the inference that Roosevelt and Captain Charles Young shared similar views about conservation? A. "Campaigns in the American West had imbued Army soldiers with the skills necessary for patrolling the vast wilderness that the new National Parks offered the public." B. 'These were areas set aside by the Federal Government to provide access to an unspoiled wilderness area, a frontier that many Americans would never be able to experience." C. "A journey through this park and the Sierra Forest Reserve to the Mount Whitney country will convince even the least thoughtulf man of the needfulness of preserving these mountains just as they are ..." D. "After making a visit to Mammoth Hot Springs in Yellowstone National Park, it was considered acceptable to chip off a piece of the travertine and to carve your name and address."