Marine losses for an oil company. The frequency distribution shown in the accompanying table depicts the property and marine losses incurred by a large oil company over a two-year period. In the insurance business, each “loss”

interval is called a layer. Research Review (Summer 1998)

demonstrated that analysts often treat the actual loss value within a layer as a uniform random variable.

a. Use the uniform distribution to find the mean loss amount in layer 2.

b. Use the uniform distribution to find the mean loss amount in layer 6.

c. If a loss occurs in layer 2, what is the probability that it exceeds $30,000?

d. If a loss occurs in layer 6, what is the probability that it is between $750,000 and $800,000?

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Marine Losses Layer ($ thousands) Relative Frequency 1234567 0-10 .927 2 10-50 .053 50-100 .010 100-250 .006 250-500 .003 500-1,000 .001 1,000-2,500 .000