Use the following scenario for questions #1 - 5. An insurance company expects 10
ID: 3202118 • Letter: U
Question
Use the following scenario for questions #1 - 5.
An insurance company expects 10% of its policyholders to collect claims of $500 this year and the remaining 90% to collect no claims
Which of the following below is a correct interpretation of the expected value in the context of this problem? SELECT ALL THAT APPLY (there is more than one correct answer).
Question 2 options:
In the long run, if you were to keep observing policy holders, the average amount the insurance company pays per person over many many people is approximately the expected value.
In the population of all policy holders, the average amount the insurance company pays per person is equal to the expected value.
If a sample of 50 policy holders were taken, the mean amount the insurance company pays per person in this sample must equal the expected value.
Every policy holder for this insurance company will be paid the expected value.
A.)In the long run, if you were to keep observing policy holders, the average amount the insurance company pays per person over many many people is approximately the expected value.
B.)In the population of all policy holders, the average amount the insurance company pays per person is equal to the expected value.
C.)If a sample of 50 policy holders were taken, the mean amount the insurance company pays per person in this sample must equal the expected value.
D.)Every policy holder for this insurance company will be paid the expected value.
Explanation / Answer
Expected Value E(X) = 0.1 x 500 + 0.9 x 0 = 50
Consider the population of size N
10% of N will claim insurance of $500
Average Amount the insurance company pays = (500 * 0.1N) / N = 50
Thus for any value of N Average (Mean) Amount = $50
In conclusion, options B and C are the correct interpretations of the Expected Value
Option A is close, but not absolutely right, since it says 'approximately'
Option D is incorrect, since policy holders with no claim will not get the Expected Value.