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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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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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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



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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