An insurance company collects premiums and pays claims and overhead expenses. A certain company has 100,000 customers (members) The net amount made (or lost) on each individual customer independently in a year is a random variable. It has a mean of $500 and a standard deviation of $8,000. $500 = (premium -expected claims paid) per member Standard deviation reflects random differences in actual claim amounts across individual members The company has fixed expenses of $45M (45,000,000) per year. The company starts the year with $K in capital reserves What is the smallest amount of money, K, that the company should have at the start the year (its capital reserve) to keep its probability of running out of money less than 1%? Assume that the company runs out of money if the sum of net amounts made or lost over all 100,000 members + K< 45,000,000 A certain company has 100,000 customers (members) The company collects a random net amount from each member independently each year, with a mean of $500 and a standard deviation of $8000. How much money, K, should the company have at the start of the year to keep P(K + sum of net amounts collected -45M 0) 0.99? Round to the nearest thousand dollars.