You are given the following information for a group of insured lives: Number of

Question

You are given the following information for a group of insured lives:

Number of lives: 1,000

Amount paid due to the occurrence of a peril: $500

Probability that peril occurs: 0.01

a. Calculate the expected value (EV) of the distribution of loss amounts.

b. Calculate the standard deviation (SD) of the distribution of loss amounts.

c. Calculate the minimum number of lives that would be needed to result in a ratio of SD/EV that is less than 0.010. (remember that the number of lives must be a whole number)

Explanation / Answer

N = 1000

n = $500, p = 0.01

a) Expected value = np = 500 * 0.01 = $5

b) standard deviation = sqrt(npq) = sqrt(500*0.01*0.99) = $2.225

c) Required frequency = 1000 * (2.225/5) = 445

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