Download TEG-Probability and Stats

PART I:
The Highway Loss Data Institute (HLDI) compiles insurance claim information
for the auto insurance industry. Data from their September 2018 report is
included below1. Use the information in the report to answer the following
question:
Acme Insurance Company has 100 customers. How
much should they charge per policy in order to break even?
Distribution of claims by
claim size
Dollar
Percentage of
amount ($) claims (%)
1,000
18.4
2,000
19.2
3,000
14.0
4,000
10.2
5,000
7.7
6,000
5.8
7,000
4.3
8,000
3.4
9,000
2.7
10,000
2.2
11,000
1.8
12,000
1.5
13,000
1.3
14,000
1.1
15,000
0.9
16,000
0.8
17,000
0.6
18,000
0.5
19,000
0.5
20,000
0.4
30,000+
2.7
Using the data from the table and graph, determine the
mean, median, and mode dollar amount per claim.
Mean:
Median:
Mode:
1Highway
Loss Data Institute (2018) Loss Facts, September 2018. Collision coverage: Distribution of collision claims by claim size, 2017 calendar
year. Retrieved from: https://www.iihs.org/media/80593d69-948a-41b8-9d4b-40d7a88055e9/t8fXYg/HLDI%20Research/Loss%20fact%20
sheets/Collision_size_2018.pdft=internal-uds-cse&cx=001263129772496713041:qpkzn11xmow&usg=AOvVaw3DoWT6bIlotYQrY9_jB-gR
Suppose Acme Insurance determines payouts to customers according to the following
criteria:
- If the claim amount is up to $2,000, they pay the full amount of the claim.
- If the claim amount is between $2,001 and $9,999, they pay $5,000.
- If the claim amount is between $10,000 and $19,999, they pay $10,000.
- If the claim amount is $20,000 or more, they pay $20,000.
Based on the HLDI data, create an outcome, probability, and value table for the
insurance payouts. Then, calculate the amount Acme Insurance must charge per policy
in order to break even.
State your answer and explain why it is true using the
table, equation and/or graph. (Make sure to provide
specific clear evidence. Use all sources (T,E,G) at least
once.)
1) The most frequent claim amount is ___________, because…
2) The average dollar amount per claim is ___________, because…
3) Acme Insurance must charge $____________ per policy, because…