An auto insurance company is implementing a new bonus system. In each month the policyholder does not have an accident, he ore she will receive 5.00 cash back bonus from the insurer. Among the 1000 policyholders of the auto insurance company, 400 are low risk drivers and 600 are high risk. The probability of a high risk driver having a accident in a given month is 0.2 and for low risk is 0.1. What is the expeccted bonus payment from the insurer to the 1000 policyholders?
I saw the solution and it gave no explanation as to why they used a poisson distribution. I cannot see why they did that a little insight would help. When should I consider using each type of distribution?