QUESTION 14 There were many car accidents following the snow in Little Rock on Jan. 6. An insurance company who offers automobile insurance had the following number of claims for the following amounts: 25 claims of \( \$ 500,12 \) claims of \( \$ 900,10 \) claims of \( \$ 1800,5 \) claims of \( \$ 2100 \) and 3 claim of \( \$ 3900 \). What was the average claim size? (please round your answer to 1 decimal place) ?

To calculate the **average claim size** for the insurance company, follow these steps: ### 1. **List the Number of Claims and Their Amounts:** - **25 claims** of **\$500** - **12 claims** of **\$900** - **10 claims** of **\$1,800** - **5 claims** of **\$2,100** - **3 claims** of **\$3,900** ### 2. **Calculate the Total Amount Claimed:** Multiply the number of claims by the amount for each category and sum them up. \[ \begin{align*} 25 \times \$500 &= \$12,500 \\ 12 \times \$900 &= \$10,800 \\ 10 \times \$1,800 &= \$18,000 \\ 5 \times \$2,100 &= \$10,500 \\ 3 \times \$3,900 &= \$11,700 \\ \hline \text{Total Amount} &= \$12,500 + \$10,800 + \$18,000 + \$10,500 + \$11,700 = \$63,500 \\ \end{align*} \] ### 3. **Calculate the Total Number of Claims:** \[ 25 + 12 + 10 + 5 + 3 = 55 \text{ claims} \] ### 4. **Determine the Average Claim Size:** \[ \text{Average Claim Size} = \frac{\text{Total Amount}}{\text{Total Number of Claims}} = \frac{\$63,500}{55} \approx \$1,154.5 \] ### **Final Answer:** The **average claim size** is **\$1,154.5**.