Vinton Auto Insurance is deciding how much money to keep in its checking accounts to cover insurance claims. In the past
Posted: Mon Jul 11, 2022 12:02 pm
Vinton Auto Insurance is deciding how much money to keep in itschecking accounts to cover insurance claims. In the past, thecompany held some of the premiums it received in interest-bearingchecking accounts and put the rest into investments that are notquite as liquid, but tend to generate a higher investment return.The company wants to study cash flows to determine how much moneyit should keep in its checking accounts to pay claims. There aretwo types of claims: “repair” claims, and “totaled” claims. Afterreviewing historical data, the company has determined that thenumber of repair claims filed each week is a random variable thatfollows the probability distribution shown in the followingtable:
# Repair 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 theaverage cost per repair claim is normallydistributed with a mean of $1,200 and standard deviation of $300(with no negative values). To be clear, the costs of covering ofeach individual repair claim are not normallydistributed; rather, the average cost per repairclaim for a given week is normally distributed with a mean of$1,200 and a standard deviation of $300. In addition to repairclaims. There is a 15% chance of receiving one claim of this typein any week, and there is no chance of receiving more than one inany week. The cost for “totaled” cars is given by the following:$7500 * X, where X is a log-normal random variable with a meanparameter of 0.15 and a standard deviation parameter of 0.5.
# Repair 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 theaverage cost per repair claim is normallydistributed with a mean of $1,200 and standard deviation of $300(with no negative values). To be clear, the costs of covering ofeach individual repair claim are not normallydistributed; rather, the average cost per repairclaim for a given week is normally distributed with a mean of$1,200 and a standard deviation of $300. In addition to repairclaims. There is a 15% chance of receiving one claim of this typein any week, and there is no chance of receiving more than one inany week. The cost for “totaled” cars is given by the following:$7500 * X, where X is a log-normal random variable with a meanparameter of 0.15 and a standard deviation parameter of 0.5.