Suppose an insurance company classifies a “serious” flood as one where at least one home that they insure is destroyed by the flood. Let Y denote the number of homes that they insure that are destroyed by a serious flood in the southern United States. The pmf for Y can be modeled by a Poisson distribution with mean 14 homes. Because of the high risk of floods in the area (and therefore cost to the customers), the insurance company offers basic and premium policies. The basic policy does not cover damage from floods, while the premium policy does. 67% of policy holders opt for the premium coverage. We will assume that flood occurrence and policyholders are independent of each other. Simulate the long term distribution for the number of homes that the company insures that will be destroyed in serious floods in the western United States. Provide the histogram for that distribution, then describe the distribution (shape, center, and spread). For each simulated value of the number of homes that were destroyed that you just found, simulate the number that were covered by a premium policy. Provide the histogram of that distribution, then describe the distribution. Use your simulated distribution to determine the probability that at least 15 homes that are destroyed are covered by a premium policy.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Suppose an insurance company classifies a “serious” flood as one where at least one home that they insure is destroyed by the flood. Let Y denote the number of homes that they insure that are destroyed by a serious flood in the southern United States. The pmf for Y can be modeled by a Poisson distribution with mean 14 homes.

Because of the high risk of floods in the area (and therefore cost to the customers), the insurance company offers basic and premium policies. The basic policy does not cover damage from floods, while the premium policy does. 67% of policy holders opt for the premium coverage. We will assume that flood occurrence and policyholders are independent of each other.

Simulate the long term distribution for the number of homes that the company insures that will be destroyed in serious floods in the western United States. Provide the histogram for that distribution, then describe the distribution (shape, center, and spread).
For each simulated value of the number of homes that were destroyed that you just found, simulate the number that were covered by a premium policy. Provide the histogram of that distribution, then describe the distribution.
Use your simulated distribution to determine the probability that at least 15 homes that are destroyed are covered by a premium policy.

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