The United Auto Courts Reports blog notes that 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 7 per day.
a. 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 (a), what is the probability that
b. 5 questionable insurance claims will be referred to investigators by Miami- Dade, Broward, and Palm Beach counties in a day?
c. 10 or fewer questionable insurance claims will be referred to investigators by Miami- Dade, Broward, and Palm Beach counties in a day?
d. 11 or more questionable insurance claims will be referred to investigators by Miami- Dade, Broward, and Palm Beach counties in a day?