Math  /  Data & Statistics

QuestionAvicenna, 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 $23,600\$ 23,600 to the policy holder. Executives at Avicenna are considering offering these policies for $791\$ 791 each. Suppose that for each holder of a policy there is a 3%3 \% chance they will experience property damage in the next five years and a 97%97 \% chance they will not.
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 \square 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.

Studdy Solution

STEP 1

1. The cost of the policy is \$791.
2. The payout for property damage is \$23,600.
3. The probability of property damage occurring is \(3\%\).
4. The probability of property damage not occurring is \(97\%\).

STEP 2

1. Calculate the expected payout for each policy.
2. Determine the expected profit or loss per policy.

STEP 3

Calculate the expected payout for property damage:
The expected payout is calculated by multiplying the probability of damage by the payout amount:
\[ \text{Expected Payout} = 0.03 \times 23,600 $
\[ \text{Expected Payout} = 708 $

STEP 4

Calculate the expected profit or loss per policy:
The expected profit or loss is the difference between the policy price and the expected payout:
\[ \text{Expected Profit/Loss} = 791 - 708 $
\[ \text{Expected Profit/Loss} = 83 $
Avicenna can expect to make money from offering these policies. In the long run, they should expect to make 83\boxed{83} dollars on each policy sold.

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