Suppose you are the risk manager for UPS and you self-insure the property - damage liability risk you face from the fleet of trucks that operate in the Southeast region. Assume each exposure's loss distribution is independent and identically distributed and, based upon historical data, you know the mean of the loss distribution for one truck is $3000 and the variance of loss is 12,000,000. Assume an actuarial consultant has concluded that you can be 99 percent certain there will be enough funds available to pay all loss obligations if you set aside the expected loss plus a 10 percent safety loading on each truck. Determine the number of trucks you have in the Southeast region.