What assumptions need to be made so that the number of questionable insurance claims referred to investigators by Miami- Dade, Broward, and Palm Beach counties is distributed as a Poisson random variable?

Exercise 1.

The National Insurance Crime Bureau says that Miami- Dade, Broward, and palm

Beach counties account for a substantial number of questionable insurance claims

referred to investigators. Assume that the number of questionable insurance claims

referred to investigators by Miami-Dade, Broward, and Palm Beach counties is

distributed as a Poisson random variable with a mean of 10 per day.

Questions:

1. What assumptions need to be made so that the number of questionable insurance claims referred to investigators by Miami- Dade, Broward, and Palm Beach counties is distributed as a Poisson random variable?

Making the assumptions given in (1), what is the probability that:

2. 5 questionable insurance claims will be referred to investigators by Miami-Dade,

Broward, and Palm Beach counties in a day?

3. 10 or fewer questionable insurance claims will be referred to investigators by

Miami-Dade, Broward, and Palm Beach counties in a day?

4. 11 or more questionable insurance claims will be referred to investigators by

Miami-Dade, Broward, and Palm Beach counties in a day?