1.Vinton Auto Insurance is deciding how much money to keep in its checking accounts 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 its checking accounts to pay claims. There are two types of claims: "repair" claims, and "totaled" claims. After reviewing historical data, the company has 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 0. 1 2 3 4. 5. 6. 7. 8. 9. 10

Probability. 0.030. 0.106. 0.185. 0.216. 0.189. 0.132 0.077. 0.039. 0.017. 0.007. 0.002

The company has also determined that theaveragecostperrepair claim is normally distributed with a mean of $1,200 and standard deviation of $300. To be clear, the costs of covering of each individual repair claim arenotnormally distributed with a mean of $1,200 and a standard deviation of $300. Rather, theaveragecost of all the repair claims for a given week is normally distributed with a mean of $1,200 and a standard deviation of $300. In addition to repair claims, the company also receives claims for cars that have been "totaled" and cannot be repaired. There is a 15% chance of receiving one claim of this type in any week, and there is no chance of receiving more than one in any week. The cost for "totaled" cars is given by the following: $7500 * X, where X is a log-normal random variable with a mean parameter of .15 and a standard deviation parameter of 0.5.

a, Develop a simulation model and report the mean total cost of all claims incurred by the company in any week. (20 points)

b, Suppose that the company decides to keep $15,000 cash on hand to pay claims. What is the probability that this amount willnotbe adequate to cover claims in any given week? (6 points)

c, What level of cash would the company have to have to be 97% certain they could pay all the claims in any given week? (6 points)