7th Edition

ISBN: 9780134684291

Author: Larson

Publisher: PEARSON CO

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Chapter 4.1, Problem 39E

Linear Transformation of a Random Variable In Exercises 39 and 40, use this information about linear transformations. For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean μ_x and standard deviation σ_x, then the mean, variance, and standard deviation of y are given by the formulas μ_y = a + bμ_x, σ²_y = b²σ²_x, and σ_Y = |b|σ_x.

39. The mean annual salary of employees at an office is originally $46,000. Each employee receives an annual bonus of $600 and a 3% raise (based on salary). What is the new mean annual salary (including the bonus and raise)?

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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Chapter 4.1, Problem 38E

Chapter 4.1, Problem 40E

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Chapter 4 Solutions

EBK ELEMENTARY STATISTICS

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Solution Summary: The author explains how the new mean annual salary, including bonus and appraisal, is 47,980. The new random variable y is obtained using the linear transformation of x.

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