Synthetic 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 less liquid investments that generate a higher return.

It has also determined that the number of repair claims filed each week is a random variable which can take values 1, 2, 4, 5, 6, 7, 8, 9. The probability of having 1 or 9 claims in a week is equal. The probability that there are 2, 6, 7 or 8 claims in a week is twice the probability of there being a single claim. The probability that there are 4 claims in a week is twice the probability that there are 2 claims in a week. The probability that there are 5 claims in a week is 6 times the probability that there is a single claim in a week. The dollar amount per claim fits a normal distribution with a mean claim amount of $2000 and a standard deviation of $400.

In addition to repair claims, the company also receives claims for cars that have been "totaled" and cannot be repaired. There is a 20% chance in any week of receiving this type of claim. The claims for "totaled" cars cost has a uniform distribution, in the range $10000 to $35000. Not all repair claims are legitimate: 1% of the repair claims filed are rejected. Of the "totaled" claims filed, 0.5% of them are rejected.

a. Create a spreadsheet model of the total claims cost incurred by the company for 100 weeks. Calculate the average payout per week. If the company decides to keep $20,000 cash on hand to pay claims, in how many of the weeks is this amount of money insufficient to pay the claims?