Question

An insurance policy for water damage pays an amount of damage up to $500. The amount of damage is uniformly distributed between $250 and $1,280. a. What is the probability that the amount of damage is more than $450? Round your answer to 3 decimals. Number b. What is the probability that the amount of damage is between $715 and $920? Round your answer to 3 decimals.

Answer #1

An insurance policy pays the loss amount up to a maximum of 500.
The loss distribution for the first policy is exponentially
distributed with mean 1000. The loss distribution for the second
policy is uniformly distributed between 0 and 1250. What is the
total insurer's expected payment for the two policies?
The result should be 793

Waterbury Insurance Company wants to study the relationship
between the amount of fire damage and the distance between the
burning house and the nearest fire station. This information will
be used in setting rates for insurance coverage. For a sample of 30
claims for the last year, the director of the actuarial department
determined the distance from the fire station (x) and the
amount of fire damage, in thousands of dollars (y). The
MegaStat output is reported below.
ANOVA table...

Waterbury Insurance Company wants to study the relationship
between the amount of fire damage and the distance between the
burning house and the nearest fire station. This information will
be used in setting rates for insurance coverage. For a sample of 30
claims for the last year, the director of the actuarial department
determined the distance from the fire station (x) and the
amount of fire damage, in thousands of dollars (y). The
MegaStat output is reported below.
ANOVA table...

Waterbury Insurance Company wants to study the relationship
between the amount of fire damage and the distance between the
burning house and the nearest fire station. This information will
be used in setting rates for insurance coverage. For a sample of 30
claims for the last year, the director of the actuarial department
determined the distance from the fire station (x) and the
amount of fire damage, in thousands of dollars (y). The
MegaStat output is reported below.
ANOVA table...

Waterbury Insurance Company wants to study the relationship
between the amount of fire damage and the distance between the
burning house and the nearest fire station. This information will
be used in setting rates for insurance coverage. For a sample of 30
claims for the last year, the director of the actuarial department
determined the distance from the fire station (X) and the
amount of fire damage, in thousands of dollars (Y). The
MegaStat output is reported below.
ANOVA table...

The probability distribution for damage claims paid by the
Newton Automobile Insurance Company on collision insurance
follows.
Payment ($)
Probability
0
0.82
500
0.05
1000
0.04
3000
0.04
5000
0.03
8000
0.01
10000
0.01
a. Use the expected collision payment to
determine the collision insurance premium that would enable the
company to break even. Answer: $
b. The insurance company charges an annual rate
of $595 for the collision coverage. What is the expected value of
the collision policy for...

Problem 5
An insurance company issues a policy on a car under the
following conditions:
(i) The replacement cost of $37,000 will be paid for a
total loss.
(ii) If it is not a total loss, but the damage is more
than $11,000, then only $ 10,500 will be paid.
(iii) Nothing will be paid for damage costing $11,000 or
less and, (iv) Nothing will be paid out if
there is no damage.
The company estimates, based on their internal...

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