Mr. Maloy has just bought a new $30,000 sport utility vehicle. As a reasonably safe driver, he believes there is only about a 5% chance of being in an accident in the coming year. If he is involved in an accident, the damage to his new vehicle depends on the severity of the accident. The probability distribution of damage amounts (in dollars) is given in the image. Mr. Maloy is trying to decide whether to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, he pays thefirst$300 in damages if he causes an accident and the insurance company pays the remainder.

Identify the decision that minimizes Mr. Maloy's annual expected cost.

Perform a sensitivity analysis on the best decision with respect to the probability of an accident, the premium, and the deductible amount, and summarize your findings. (You can choose the ranges to test.)

1 Distribution of damage amount, given that an accident has occurred 2 3 Accident type Probability Damage to vehicle 4 Minor 0,6 $200 5 Moderate 0,2 $1.000 6 Serious 0,1 $4.000 7 Catastrophic 0, 1 $30.000 8