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Get Full Access to Statistics For Business And Economics - 12 Edition - Chapter 4 - Problem 146e
Get Full Access to Statistics For Business And Economics - 12 Edition - Chapter 4 - Problem 146e

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# Marine losses for an oil company. The frequency

ISBN: 9780321826237 51

## Solution for problem 146E Chapter 4

Statistics for Business and Economics | 12th Edition

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Problem 146E

Problem 146E

Marine losses for an oil company. The frequency distribution shown in the next table depicts the property and marine losses incurred by a large oil company over the last 2 years. This distribution can be used by the company to predict future losses and to help determine an appropriate level of insurance coverage. In analyzing the losses within an interval of the distribution, for simplification, analysts may treat the interval as a uniform probability distribution (Research Review, Summer 1998). In the insurance business, intervals like these are often called layers.

 Layer Property and MarineLosses (millions of \$) Frequency 1 0.00–0.01 668 2 0.01–0.05 38 3 0.05–0.10 7 4 0.10–0.25 4 5 0.25–0.50 2 6 0.50–1.00 1 7 1.00–2.50 0

Source: Based on Cozzolino, J. M., & Mikolaj, P. J. “Applications of the piecewise constant pareto distribution,” Research Review, Summer 1998, pp. 39–59.

a. Use a uniform distribution to model the loss amount in layer 2. Graph the distribution. Calculate and interpret its mean and variance.

b. Repeat part a for layer 6.

c. If a loss occurs in layer 2, what is the probability that it exceeds \$10,000? That it is under \$25,000?

d. If a layer-6 loss occurs, what is the probability that it is between \$750,000 and \$1,000,000? That it exceeds \$900,000? That it is exactly \$900,000?

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