Pablo traded in his 2000 Ford for a new Ford. One week later, he hit an oily spot in the road on his way to work and skidded into a parked car. The 2000 Ford was insured under the PAP with full coverage, including a $250 deductible for a collision loss. At the time of the accident, Pablo had not notified his insurer of the trade-in. The physical damage to the parked car was$8000. Damage to Pablo’s car was $5000. Will Pablo’s PAP cover either or both of these losses? Explain.

The PAP provides liability coverage to four groups. Identify the four groups of persons or parties who can be insured under the PAP.

Janet has a PAP with the following coverages:

• Liability coverages: $100,000/$300,000/$50,000
• Medical payments coverage:$5000 each person
• Uninsured motorists coverage: $25,000 each person
• Collision loss:$250 deductible
• Other-than-collision loss: $100 deductible
• Towing and labor cost coverage:$75 each disablement

To what extent, if any, is each of the following losses covered under Janet’s PAP? Treat each event separately.

• a. Janet rents a car while on vacation. She is involved in an accident with another motorist when she fails to yield the right of way. The injured motorist is awarded a judgment of $100,000. The rental agency carries only liability limits of$30,000 on the rental car. The rental agency carries no collision insurance on its cars and is seeking $15,000 from Janet for repairs to the rental car.
• b. Janet borrows her friend’s car with permission. Janet is in an accident with another motorist in which she is at fault. The cost of repairing the friend’s car is$5000. The friend’s auto policy has a $500 deductible for collision losses and$100 for other-than-collision losses.
• c. Janet is employed as a salesperson and is furnished a company car. She is involved in an accident with another motorist while driving the company car during business hours. The injured motorist claims Janet is at fault and sues her for $100,000. Damage to the company car amounts to$5000.
• d. Janet’s car will not start because of a defective battery. A tow truck brings the car to a service station where the battery is replaced. Towing charges are $60. The cost of replacing the battery is$100.

For a chi-squared distribution, find (a) $\chi^2_{0.025}$ when v = 15; (b) $\chi^2_{0.01}$ when v = 7; (c) $\chi^2_{0.05}$ when v = 24;

Karen is the named insured under a PAP that provides coverage for bodily injury and property damage liability, medical payments, and uninsured motorists coverage. For each of the following situations, briefly explain whether the claim is covered by Karen’s PAP.

• a. Karen ran into a telephone pole and submitted a medical expense claim for Jason, a passenger in Karen’s car at the time of the accident.
• b. Karen allowed Scott to use her car. While operating Karen’s car, Scott damaged Gray’s car in an accident caused by Scott’s negligence. Karen is sued by Gray for damages.
• c. Karen’s husband ran over a bicycle while driving a friend’s car. The owner of the bicycle demands that Karen’s husband pay for the damage.
• d. In a fit of anger, Karen deliberately ran over the wagon of a neighbor’s child that had been left in Karen’s driveway after repeated requests that the wagon be left elsewhere. The child’s parents seek reimbursement.

The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mean of 28 centimeters with a standard deviation of 5 centimeters. Assuming that the sample means can be measured to any degree of accuracy, find the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at most 44.2 centimeters.

The average life of a bread-making machine is 7 years, with a standard deviation of 1 year. Assuming that the lives of these machines follow approximately a normal distribution, find (a) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2 years; (b) the value of $x$ to the right of which 15$\%$ of the means computed from random samples of size 9 would fall.

If a certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms, what is the probability that a random sample of 36 of these resistors will have a combined resistance of more than 1458 ohms?

Given a normal random variable X with mean 20 and variance 9, and a random sample of size n taken from the distribution, what sample size n is necessary in order that

$$P(19.9 \leq \hat{X} \leq 20.1) = 0.95?$$

The PAP provides coverage for your covered auto. Identify the four classes of vehicles that are considered to be covered autos.

Does the PAP cover you if you are driving a vehicle in a foreign country? Explain your answer.

The Personal Auto Policy (PAP) contains several coverages that meet the insurance needs of typical insureds. For each of the following coverages, briefly describe the type of coverage provided, and give an example of a loss that would be covered.

• a. Part A: Liability Coverage
• b. Part B: Medical Payments Coverage
• c. Part C: Uninsured Motorists Coverage
• d. Part D: Coverage for Damage to Your Auto

Fred has a PAP with the following coverages:

• Liability coverages: $100,000/$300,000/$50,000
• Medical payments coverage:$5000 each person
• Uninsured motorists coverage: $25,000 each person
• Collision loss:$250 deductible
• Other-than-collision loss: $100 deductible

With respect to each of the following situations, indicate whether the loss is covered and the amount payable, if any, under the policy. Assume that each situation is a separate event.

• a. Fred’s son, age 16, is driving a family car, runs a red light, and kills a pedestrian. The family of the deceased pedestrian sues and damages are awarded in the amount of$500,000.
• b. Fred borrows a friend’s car to go to the supermarket. He fails to stop at a red light and negligently smashes into another motorist. The other driver’s car, valued at $15,000, is totally destroyed. In addition, repairs to the friend’s car are$5000.
• c. Fred’s daughter, Heather, attends college in another state and drives a family auto. Heather lets her boyfriend drive the car, and he negligently injures another motorist. The boyfriend is sued for $50,000.
• d. Fred’s wife is driving a family car in a snowstorm. She loses control of the car on an icy street and smashes into the foundation of a house. The property damage to the house is$30,000. The damage to the family car is $8000. Fred’s wife has medical expenses of$5000.
• e. Fred is walking across a street and is struck by a motorist who fails to stop. He has bodily injuries in the amount of $15,000.
• f. Fred’s car is being repaired for faulty brakes. While road-testing the car, a mechanic injures another motorist and is sued for$50,000.
• g. Fred’s car hits a cow crossing a highway. The cost of repairing the car is $2500.
• h. A thief breaks a car window and steals a camera and golf clubs locked in the car. It will cost$400 to replace the damaged window. The stolen property is valued at $500.
• i. Fred’s wife goes shopping at a supermarket. When she returns, she finds that the left rear fender has been damaged by another driver who did not leave a name. The cost of repairing the car is$2000.
• j. Fred works for a construction company. While driving a large cement truck, he negligently injures another motorist. The injured motorist sues Fred for $25,000.
• k. Fred’s son drives a family car on a date. He gets drunk, and his girlfriend drives him home. The girlfriend negligently injures another motorist, who has bodily injuries in the amount of$200,000.
• l. Compact discs (CDs) valued at $500 are stolen from Fred’s car. The car was locked when the theft occurred.
• m. While driving a rented golf cart, Fred accidentally injures another golfer with the cart.

Kim, age 20, is a college student who recently purchased her first car from a friend who had financial problems. The vehicle is a high mileage, 2001 Toyota Corolla with a current market value of $2000. Assume you are a financial planner and Kim asks your advice concerning the various coverages in the PAP.

• a. Briefly describe the major coverages that are available in the PAP.
• b. Which of the available coverages in (a) should Kim purchase? Justify your answer.
• c. Which of the available coverages in (a) should Kim not purchase? Justify your answer.
• d. Assume that Kim purchases the PAP coverages that you have recommended. To what extent, if any, would Kim’s insurance cover the following situations?

1. Danielle, Kim’s roommate, borrows Kim’s car with her permission and injures another motorist. Danielle is at fault.
2. Kim is driving under the influence of alcohol and is involved in an accident where another motorist is seriously injured.
3. During the football season, Kim charges a fee to transport fans from a local bar to the football stadium. Several passengers are injured when Kim suddenly changes lanes without signaling and hits another car.
4. Kim drives her boyfriend’s car on a regular basis. While driving the boyfriend’s car, she is involved in an accident in which another motorist is injured. Kim is at fault.
5. Kim rents a car in England where she is participating in a summer study program. The car is stolen from a dormitory parking lot.

• e. Kim also owns a motorcycle. To what extent, if any, does Kim’s PAP cover the motorcycle?