Answered: An auto insurance company tracks the…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 8SGR

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Question

An auto insurance company tracks the experience of its first-year and multi-year policyholders
separately. First-year policyholders account for 15% of the company's business while multi-year
policyholders account for the rest.
The number of claims reported to the company in a year by a first-year policyholder follows a Poisson
distribution with mean 0.60, while the number of claims reported to the company in a year by a multi-
year policyholder follows a Poisson distribution with mean 0.30.
Calculate the probability that a policyholder is a first-year policyholder, given that the policyholder
reports exactly three claims in an eight-months period to the company

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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