Final answer:
The expected cost of accidents per driver is $1,452.20, and when adding the overhead cost of $115, the total cost that the insurance premium should cover is $1,567.20. The closest given option is $1,565.48, which is slightly lower than the calculated premium but would be chosen to ensure costs are covered.
Step-by-step explanation:
To determine the driver's insurance premium, we need to calculate the expected cost to the insurance company per driver and add the overhead cost.
The expected cost per driver is the product of the probability of getting into an accident (8.6%) and the average cost of such an accident ($16,886.05). Therefore, multiplying 0.086 by $16,886.05 equals $1,452.20, which represents the expected cost of accidents per driver.
Next, we add the overhead cost of $115 per insured driver to the expected cost of accidents to find the total cost that needs to be covered by the insurance premium. So, $1,452.20 (expected accidents cost) + $115 (overhead cost) equals $1,567.20.
However, given the options provided, none of them match exactly our calculation.
The closest option and the one that would ensure the insurance company covers the calculated costs without a loss is $1,565.48 (Option D).
Note that actual insurance premiums often include additional factors for profit margin, administrative fees, and potential unanticipated costs, which are not accounted for in this simple calculation.