HW 6 Key

9:55 4M Credit Scores. An insurance agent has just opened an office in a community. Conversations with the local bank produced the distribution of scores shown in this table. The table also shows the cost of car insurance.

9:55 a Motivation. The insurance agent is paid by commission, earning 10% of the annual premium. Why should the agent care about the expected value of a random variable? Since the agent is paid by commission, selling high premium policies is worth more than less expensive policies.

9:55 b b. Why should the agent also care about the variance and standard deviation? These are only probabilities, so the results will vary around the mean. The SD indicates roughly how far from the mean the results could be.

9:55 c c. Method. Identify the random variable described in this table that is most relevant to the agent. X = annual premium for random customer

9:55 d d. How is this random variable related to his commission? C = commission from a policy C = 0.1*X

9:55 e e. Mechanics. Graph the probability distribution of the random variable of interest to the agent.

9:55 f f. Find the expected commission earned by the agent for writing one policy. 665*.1 = $66.50

9:55 g g. Find the variance and standard deviation of the commission earned by the agent for writing one policy. SD = $270.69 270.69*.1 = $27.07

9:55 h h. Message. Summarize your results for the agent in everyday language. The agent can expect to earn on average about $66 for each policy sold but with quite a bit of variation. The agent can expect 60% of the policies sold to earn him $50. He can expect 15% of the policies he sells to pay more than $100.

9:55 i Do you have any advice for the insurance company based on these calculations? Because the agent is paid by commission and hence earns the most by finding riskier customers, managers at the insurance company should not be surprised if they find the agent writes more risky policies. The agent earns $150 for the most risky policies, compared to $50 for the best policies.