Download 6 - Marriott School

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
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
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.