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Lee Colle insures its students for thefts up to $1000. The college mak 04 Dec 2019, 00:52
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33% (02:17) correct 67% (02:35) wrong based on 147 sessions

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Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


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Lee Colle insures its students for thefts up to $1000. The college mak 04 Dec 2019, 13:07
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Bunuel
Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


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I got the expected number of thefts is 200 and feel free to correct me if I'm not understanding properly.

The $1000 is merely a distractor. For every 100 people, the cost of the insurance is n * 120, where n is the number of claims expected from every 100 students. The revenue is 100 * 24 = 2400. So we should get 10% * Cost = Revenue according to the problem.

10% * n * 120 = 2400
12n = 2400
n = 200
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Lee Colle insures its students for thefts up to $1000. The college mak 08 Dec 2019, 12:48
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Bunuel
Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


I got the expected number of thefts is 200 and feel free to correct me if I'm not understanding properly.

The $1000 is merely a distractor. For every 100 people, the cost of the insurance is n * 120, where n is the number of claims expected from every 100 students. The revenue is 100 * 24 = 2400. So we should get 10% * Cost = Revenue according to the problem.

10% * n * 120 = 2400
12n = 2400
n = 200
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I had the same answer. Although I think the issue is that the administration is providing the entire insurance so they are paying out the claim in addition to the administration fee. If that is the case, it is fairly unclear and becomes more about understanding how insurance works.

1.10 * n * 120 = 2400
132 * n = 2400
n ~ 18
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Lee Colle insures its students for thefts up to $1000. The college mak 19 Feb 2020, 09:57
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According to the question the total revenue is equal to the total cost which makes the profit zero. Let's assume the number of thefts per year is n, then

Total revenue is 24*100 and total cost is 10% of the n*120 because the average claim is given as 120 + n*120 which is the amount that should be submitted to the students according to the insurance policy.

24*100 = 120*n + 12*n

n is slightly larger than 18. 18 is the closest amongst the options.

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Lee Colle insures its students for thefts up to $1000. The college mak 24 May 2020, 04:46
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total cost per claim= 120 $ + (10% of 120 $) = 132 $

Cost of premium incurred by 100 students = 100 *24 = 2400

Now no profit is earned by university.

2400 = 132 * k (where K is no. of claims filed per 100 students in year on average)

K= 2400/132 ~ 18.**

So, our reqd. answer = 18

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Lee Colle insures its students for thefts up to $1000. The college mak 05 Jun 2020, 11:44
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Bunuel
Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


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We can let 100 be the number of students in this college and n be the number of thefts. Furthermore, we can see that the administrative costs are $12 per theft; therefore, we have:

Total payout + Total admin. costs = Total revenue

120n + 12n = 24 x 100

132n = 2400

n = 2400/132 ≈ 18

Answer: D
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Lee Colle insures its students for thefts up to $1000. The college mak 20 Mar 2025, 02:30
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