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(solution) Auto Insurance is trying to decide how much money to keep in


Auto Insurance is trying to decide how much money to keep in liquid assets to cover insurance claims. In the past, the company held some of the premiums it received in interest-bearing checking accounts and put the rest into investments that are not quite as liquid but tend to generate a higher investment return. The company wants to study cash flows to determine how much money it should keep in liquid assets to pay claims. After reviewing historical data, the company determined that the average repair bill per claim is normally distributed with a mean of $1,700 and standard deviation of $400. It also determined that the number of repair claims filed each week is a random variable that follows the probability distribution shown in the following table:

Number of claims

1

2

3

4

5

6

7

8

9

probability

0.05

0.06

0.10

0.17

0.28

0.14

0.08

0.07

0.05

In addition to repair claims, the company also receives claims for cars that have been ?totaled? and cannot be repaired. A20% chance of receiving this type of claim exists in any week. These claims for ?totaled? cars typically cost anywhere from $2,000 to $35,000, with $13,000 being the most common cost.

(a) Create a spreadsheet model of the total claims cost incurred by the company in any week.

(b) Create a histogram of the distribution of total cost values that were generated.

(c) What is the average cost the company should expect to pay each week?

(d) Suppose that the company decides to keep $20,000 cash on hand to pay claims. What is the probability that this amount would not be adequate to cover claims in any week?

(e) Create a 95% confidence interval for the true probability of claims exceeding $20,000 in a given week.

 


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