Answered: In 2007, the mean property crime rate…

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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In 2007, the mean property crime rate (per 100,000 people) for the 24 states west of a certain river was 3329.The standard deviation was 704.
Assume the distribution of crime rates is unimodal and symmetric. Complete parts a through c below.

What percentage of western states would you expect to have property crime rates between 2625 and 4033?

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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Given

In 2007, the mean property crime rate (per 100,000 people) for the 24 states west of a certain river was 3329.The standard deviation was 704.

Let X: Crime rates

And X follow normal distribution with mean =3329 and standard deviation = 704.

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