An insurance company estimates that the annual number of car accidents for a group of drivers follows
Question:
An insurance company estimates that the annual number of car accidents for a group of drivers follows a Poisson distribution with a mean of 3 accidents per year. The company offers two insurance policies: Policy A with a premium of $100 per year and covers up to 2 accidents per year, and Policy B with a premium of $200 per year and covers up to 4 accidents per year. Assuming that the only cost to the company is the amount paid to policyholders for their claims, answer the following questions:
a) What is the expected value and the standard deviation of the number of accidents per year?
b) What is the probability that a driver with Policy A will have no claims in a year?
c) What is the expected amount of claims per year for a driver with Policy A?
d) What is the expected amount of claims per year for a driver with Policy B?
Data Analysis and Decision Making
ISBN: 978-0538476126
4th edition
Authors: Christian Albright, Wayne Winston, Christopher Zappe